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  • HARISH-CHANDRA BIMODULES OVER QUANTIZED SYMPLECTIC SINGULARITIES
    Transform. Groups (IF 0.75) Pub Date : 2021-01-09
    I. LOSEV

    In this paper we classify the irreducible Harish-Chandra bimodules with full support over filtered quantizations of conical symplectic singularities under the condition that none of the slices to codimension 2 symplectic leaves has type E8. More precisely, consider the quantization 𝒜⋋ with parameter ⋋. We show that the top quotient \( \overline{\mathrm{HC}}\left(\mathcal{A}\lambda \right) \) of the

    更新日期:2021-01-15
  • THE CATEGORY OF WEIGHT MODULES FOR SYMPLECTIC OSCILLATOR LIE ALGEBRAS
    Transform. Groups (IF 0.75) Pub Date : 2021-01-09
    GENQIANG LIU, KAIMING ZHAO

    The rank n symplectic oscillator Lie algebra 𝔤n is the semidirect product of the symplectic Lie algebra 𝔰𝔭2n and the Heisenberg algebra Hn. In this paper, we first study weight modules with finite-dimensional weight spaces over 𝔤n. When the central charge \( \dot{z} \) ≠ 0, it is shown that there is an equivalence between the full subcategory 𝒪𝔤n \( \left[\dot{z}\right] \) of the BGG category

    更新日期:2021-01-15
  • CLASSIFICATION OF 3-GRADED CAUSAL SUBALGEBRAS OF REAL SIMPLE LIE ALGEBRAS
    Transform. Groups (IF 0.75) Pub Date : 2021-01-08
    D. OEH

    Let (\( \mathfrak{g} \), τ) be a real simple symmetric Lie algebra and let W ⊂ \( \mathfrak{g} \) be an invariant closed convex cone which is pointed and generating with τ(W) = −W. For elements h ∈ \( \mathfrak{g} \) with τ(h) = h, we classify the Lie algebras \( \mathfrak{g} \)(W, τ, h) which are generated by the closed convex cones \( {C}_{\pm}\left(W,\tau, h\right):= \left(\pm W\right)\cap {\mathfrak{g}}_{\pm

    更新日期:2021-01-08
  • FACTORIAL AFFINE G α -VARIETIES ISOMORPHIC TO HYPERSURFACES OF DANIELEWSKI TYPE
    Transform. Groups (IF 0.75) Pub Date : 2020-11-18
    KAYO MASUDA

    Let k be an algebraically closed field of characteristic zero and B a factorial affine k-domain equipped with a locally nilpotent derivation δ. We investigate B when there exists an element z ∈ B such that δ(z) = αp for p ≥ 1 and a prime element α of A = Ker δ. One such example of particular interest is the coordinate ring of an affine pseudo-n-space, which is defined as a smooth affine variety X equipped

    更新日期:2021-01-08
  • Algebraic Groups Whose Orbit Closures Contain Only Finitely Many Orbits
    Transform. Groups (IF 0.75) Pub Date : 2021-01-02
    VLADIMIR L. POPOV

    We explore connected affine algebraic groups G, which enjoy the following finiteness property (F): for every algebraic action of G, the closure of every G-orbit contains only finitely many G-orbits. We obtain two main results. First, we classify such groups. Namely, we prove that a connected affine algebraic group G enjoys property (F) if and only if G is either a torus or a product of a torus and

    更新日期:2021-01-02
  • A COMBINATORIAL STUDY OF AFFINE SCHUBERT VARIETIES IN THE AFFINE GRASSMANNIAN
    Transform. Groups (IF 0.75) Pub Date : 2021-01-02
    MARC BESSON, JIUZU HONG

    Let \( {\overline{\mathrm{X}}}_{\uplambda} \) be the closure of the I-orbit \( {\overline{\mathrm{X}}}_{\uplambda} \) in the affine Grassmanian Gr of a simple algebraic group G of adjoint type, where I is the Iwahori subgroup and λ is a coweight of G. We find a simple algorithm which describes the set Ψ(λ) of all I-orbits in \( {\overline{\mathrm{X}}}_{\uplambda} \) in terms of coweights. We introduce

    更新日期:2021-01-02
  • VOLUMES OF TWO-BRIDGE CONE MANIFOLDS IN SPACES OF CONSTANT CURVATURE
    Transform. Groups (IF 0.75) Pub Date : 2020-11-24
    A. D. MEDNYKH

    We investigate the existence of hyperbolic, spherical or Euclidean structure on cone-manifolds whose underlying space is the three-dimensional sphere and singular set is a given two-bridge knot. For two-bridge knots with not more than 7 crossings we present trigonometrical identities involving the lengths of singular geodesics and cone angles of such cone-manifolds. Then these identities are used to

    更新日期:2020-11-25
  • A MATSUMOTO–MOSTOW RESULT FOR ZIMMER’S COCYCLES OF HYPERBOLIC LATTICES
    Transform. Groups (IF 0.75) Pub Date : 2020-11-17
    M. MORASCHINI, A. SAVINI

    Following the philosophy behind the theory of maximal representations, we introduce the volume of a Zimmer’s cocycle Γ × X → PO° (n, 1), where Γ is a torsion-free (non-)uniform lattice in PO° (n, 1), with n > 3, and X is a suitable standard Borel probability Γ-space. Our numerical invariant extends the volume of representations for (non-)uniform lattices to measurable cocycles and in the uniform setting

    更新日期:2020-11-17
  • q -SCHUR ALGEBRAS CORRESPONDING TO HECKE ALGEBRAS OF TYPE B
    Transform. Groups (IF 0.75) Pub Date : 2020-10-31
    CHUN-JU LAI, DANIEL K. NAKANO, ZIQING XIANG

    In this paper the authors investigate the q-Schur algebras of type B that were constructed earlier using coideal subalgebras for the quantum group of type Α. The authors present a coordinate algebra type construction that allows us to realize these q-Schur algebras as the duals of the dth graded components of certain graded coalgebras. Under suitable conditions an isomorphism theorem is proved that

    更新日期:2020-11-16
  • RIGIDITY OF FLAG SUPERMANIFOLDS
    Transform. Groups (IF 0.75) Pub Date : 2020-11-13
    E. G. VISHNYAKOVA

    We prove that under certain assumptions a supermanifold of flags is rigid, that is, its complex structure does not admit any non-trivial small deformation. Moreover under the same assumptions we show that a supermanifold of flags is a unique non-split supermanifold with given retract.

    更新日期:2020-11-13
  • ADJUNCTION FOR VARIETIES WITH A ℂ* ACTION
    Transform. Groups (IF 0.75) Pub Date : 2020-11-11
    ELEONORA A. ROMANO, JAROSŁAW A. WIŚNIEWSKI

    Let X be a complex projective manifold, L an ample line bundle on X, and assume that we have a ℂ* action on (X;L). We classify such triples (X; L;ℂ*) for which the closure of a general orbit of the ℂ* action is of degree ≤ 3 with respect to L and, in addition, the source and the sink of the action are isolated fixed points, and the ℂ* action on the normal bundle of every fixed point component has weights

    更新日期:2020-11-12
  • TOPOLOGICAL LOOPS HAVING SOLVABLE INDECOMPOSABLE LIE GROUPS AS THEIR MULTIPLICATION GROUPS
    Transform. Groups (IF 0.75) Pub Date : 2020-11-06
    Á. FIGULA, A. AL-ABAYECHI

    We prove that the solvability of the multiplication group Mult(L) of a connected simply connected topological loop L of dimension three forces that L is classically solvable. Moreover, L is congruence solvable if and only if either L has a non-discrete centre or L is an abelian extension of a normal subgroup ℝ by the 2-dimensional nonabelian Lie group or by an elementary filiform loop. We determine

    更新日期:2020-11-06
  • TWISTED CONJUGACY IN LINEAR ALGEBRAIC GROUPS
    Transform. Groups (IF 0.75) Pub Date : 2020-10-31
    S. BHUNIA, A. BOSE

    Let k be an algebraically closed field, G a linear algebraic group over k and φ ∈ Aut(G), the group of all algebraic group automorphisms of G. Two elements x; y of G are said to be φ-twisted conjugate if y = gxφ(g)–1 for some g ∈ G. In this paper we prove that for a connected non-solvable linear algebraic group G over k, the number of its φ-twisted conjugacy classes is infinite for every φ ∈ Aut(G)

    更新日期:2020-11-02
  • OBSTRUCTIONS TO FREE ACTIONS ON BAZAIKIN SPACES
    Transform. Groups (IF 0.75) Pub Date : 2020-10-27
    E. KHALILI SAMANI

    Apart from spheres and an infinite family of manifolds in dimension seven, Bazaikin spaces are the only known examples of simply connected Riemannian manifolds with positive sectional curvature in odd dimensions. We consider positively curved Riemannian manifolds whose universal covers have the same cohomology as Bazaikin spaces and prove structural results for the fundamental group in the presence

    更新日期:2020-10-30
  • CRYSTAL STRUCTURES FOR SYMMETRIC GROTHENDIECK POLYNOMIALS
    Transform. Groups (IF 0.75) Pub Date : 2020-10-26
    CARA MONICAL, OLIVER PECHENIK, TRAVIS SCRIMSHAW

    The symmetric Grothendieck polynomials representing Schubert classes in the Ktheory of Grassmannians are generating functions for semistandard set-valued tableaux. We construct a type An crystal structure on these tableaux. This crystal yields a new combinatorial formula for decomposing symmetric Grothendieck polynomials into Schur polynomials. For single-columns and single-rows, we give a new combinatorial

    更新日期:2020-10-30
  • ON THE REGULARITY OF D -MODULES GENERATED BY RELATIVE CHARACTERS
    Transform. Groups (IF 0.75) Pub Date : 2020-10-24
    WEN-WEI LI

    Following the ideas of Ginzburg, for a subgroup K of a connected reductive ℝ-group G we introduce the notion of K-admissible D-modules on a homogeneous G-variety Z. We show that K-admissible D-modules are regular holonomic when K and Z are absolutely spherical. This framework includes: (i) the relative characters attached to two spherical subgroups H1 and H2, provided that the twisting character χi

    更新日期:2020-10-30
  • THE COMPONENTS OF THE SINGULAR LOCUS OF A COMPONENT OF A SPRINGER FIBER OVER x 2 = 0
    Transform. Groups (IF 0.75) Pub Date : 2020-10-02
    RONIT MANSOUR, ANNA MELNIKOV

    For x ∈ End(𝕂n) satisfying x2 = 0 let ℱx be the variety of full flags stable under the action of x (Springer fiber over x). The full classification of the components of ℱx according to their smoothness was provided in [4] in terms of both Young tableaux and link patterns. Moreover in [2] the purely combinatorial algorithm to compute the singular locus of a singular component of ℱx is provided. However

    更新日期:2020-10-20
  • GELFAND–TSETLIN DEGENERATIONS OF REPRESENTATIONS AND FLAG VARIETIES
    Transform. Groups (IF 0.75) Pub Date : 2020-10-14
    I. MAKHLIN

    Our main goal is to show that the Gelfand–Tsetlin toric degeneration of the type A ag variety can be obtained within a degenerate representation-theoretic framework similar to the theory of PBW degenerations. In fact, we provide such frameworks for all Gröbner degenerations intermediate between the ag variety and the GT toric variety. These degenerations are shown to induce filtrations on the irreducible

    更新日期:2020-10-14
  • THE GROTHENDIECK–SERRE CONJECTURE OVER SEMILOCAL DEDEKIND RINGS
    Transform. Groups (IF 0.75) Pub Date : 2020-10-03
    N. GUO

    For a reductive group scheme G over a semilocal Dedekind ring R with total ring of fractions K, we prove that no nontrivial G-torsor trivializes over K. This generalizes a result of Nisnevich–Tits, who settled the case when R is local. Their result, in turn, is a special case of a conjecture of Grothendieck–Serre that predicts the same over any regular local ring. With a patching technique and weak

    更新日期:2020-10-04
  • SUZUKI FUNCTOR AT THE CRITICAL LEVEL
    Transform. Groups (IF 0.75) Pub Date : 2020-10-03
    T. PRZEŹDZIECKI

    In this paper we define and study a critical-level generalization of the Suzuki functor, relating the affine general linear Lie algebra to the rational Cherednik algebra of type A. Our main result states that this functor induces a surjective algebra homomorphism from the centre of the completed universal enveloping algebra at the critical level to the centre of the rational Cherednik algebra at t

    更新日期:2020-10-04
  • SMOOTHNESS CONDITIONS IN COHOMOGENEITY ONE MANIFOLDS
    Transform. Groups (IF 0.75) Pub Date : 2020-09-26
    L. VERDIANI, W. ZILLER

    We present an efficient method for determining the conditions that a metric on a cohomogeneity one manifold, defined in terms of functions on the regular part, needs to satisfy in order to extend smoothly to the singular orbit.

    更新日期:2020-09-26
  • ON SOME VERTEX ALGEBRAS RELATED TO V − 1 sl n $$ {V}_{-1}\left(\mathfrak{sl}(n)\right) $$ AND THEIR CHARACTERS
    Transform. Groups (IF 0.75) Pub Date : 2020-09-10
    DRAŽEN ADAMOVIĆ, ANTUN MILAS

    We consider several vertex operator algebras and superalgebras closely related to \( {V}_{-1}\left(\mathfrak{sl}(n)\right) \), n ≥ 3 : (a) the parafermionic subalgebra K(\( \mathfrak{sl} \)(n); −1) for which we completely describe its inner structure, (b) the vacuum algebra Ω(V−1(\( \mathfrak{sl} \)(n))), and (c) an infinite extension \( \mathcal{U} \) of V−1(\( \mathfrak{sl} \)(n)) obtained from certain

    更新日期:2020-09-10
  • ON THE BOUNDED DERIVED CATEGORY OF IGr(3, 7)
    Transform. Groups (IF 0.75) Pub Date : 2020-09-08
    A. FONAREV

    We construct a minimal Lefschetz decomposition of the bounded derived category of coherent sheaves on the isotropic Grassmannian IGr(3, 7). Moreover, we show that IGr(3, 7) admits a full exceptional collection consisting of equivariant vector bundles.

    更新日期:2020-09-08
  • QUANTUM TORIC DEGENERATION OF QUANTUM FLAG AND SCHUBERT VARIETIES
    Transform. Groups (IF 0.75) Pub Date : 2020-09-08
    L. RIGAL, P. ZADUNAISKY

    We show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen–Macaulay, can be tested by passing to associated graded rings. In the spirit of noncommutative algebraic geometry, this can be seen as an analogue of the classical result that, in a flat family of varieties over the affine line, regularity properties of the exceptional fiber

    更新日期:2020-09-08
  • EXOTIC SPRINGER FIBERS FOR ORBITS CORRESPONDING TO ONE-ROW BIPARTITIONS
    Transform. Groups (IF 0.75) Pub Date : 2020-09-08
    N. SAUNDERS, A. WILBERT

    We study the geometry and topology of exotic Springer fibers for orbits corresponding to one-row bipartitions from an explicit, combinatorial point of view. This includes a detailed analysis of the structure of the irreducible components and their intersections as well as the construction of an explicit affine paving. Moreover, we compute the ring structure of cohomology by constructing a CW-complex

    更新日期:2020-09-08
  • SIMPLE BOUNDED HIGHEST WEIGHT MODULES OF BASIC CLASSICAL LIE SUPERALGEBRAS
    Transform. Groups (IF 0.75) Pub Date : 2020-09-08
    MARIA GORELIK, DIMITAR GRANTCHAROV

    We classify all simple bounded highest weight modules of a basic classical Lie superalgebra \( \mathfrak{g} \). In particular, our result leads to the classification of the simple weight modules with finite weight multiplicities over all classical Lie superalgebras. We also obtain some character formulas of strongly typical bounded highest weight modules of \( \mathfrak{g} \).

    更新日期:2020-09-08
  • THE COHEN–MACAULAY PROPERTY OF INVARIANT RINGS OVER THE INTEGERS
    Transform. Groups (IF 0.75) Pub Date : 2020-09-02
    AREEJ ALMUHAIMEED

    We prove various characterisations for the Cohen–Macaulay property for the invariant ring k[x1, …, xn]G, where k is a PID.We also show that, except for one case, all the invariant rings ℤ[x1, x2]G and ℤ[x1, x2, x3]G are Cohen–Macaulay. We also provide some sufficient conditions to obtain a polynomial invariant ring over the ring of integers.

    更新日期:2020-09-02
  • HOMOGENEOUS RIEMANNIAN MANIFOLDS WITH NON-TRIVIAL NULLITY
    Transform. Groups (IF 0.75) Pub Date : 2020-09-02
    A. J. DI SCALA, C. OLMOS, F. VITTONE

    We develop a general theory for irreducible homogeneous spaces M = G/H, in relation to the nullity distribution ν of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that give a deep insight of such spaces. In particular, there must exist an order-two transvection, not in the nullity, with null Jacobi operator. This fact was

    更新日期:2020-09-02
  • TAME DISCRETE SETS IN ALGEBRAIC GROUPS
    Transform. Groups (IF 0.75) Pub Date : 2020-08-28
    J. WINKELMANN

    Rosay and Rudin introduced the notion of tame discrete subsets of the affine complex space and investigated their properties. We generalize this theory to the case of a complex linear algebraic group with trivial character group.

    更新日期:2020-08-28
  • EQUIVARIANT DERIVED CATEGORIES FOR TOROIDAL GROUP IMBEDDINGS
    Transform. Groups (IF 0.75) Pub Date : 2020-08-26
    ROY JOSHUA

    Let X denote a projective variety over an algebraically closed field on which a linear algebraic group acts with finitely many orbits. Then, a conjecture of Soergel and Lunts in the setting of Koszul duality and Langlands' philosophy, postulates that the equivariant derived category of bounded complexes with constructible equivariant cohomology sheaves on X is equivalent to a full subcategory of the

    更新日期:2020-08-26
  • HOLONOMY AND 3-SASAKIAN HOMOGENEOUS MANIFOLDS VERSUS SYMPLECTIC TRIPLE SYSTEMS
    Transform. Groups (IF 0.75) Pub Date : 2020-08-26
    C. DRAPER

    Our aim is to support the choice of two remarkable connections with torsion in a 3-Sasakian manifold, proving that, in contrast to the Levi-Civita connection, the holonomy group in the homogeneous cases reduces to a proper subgroup of the special orthogonal group, of dimension considerably smaller. We realize the computations of the holonomies in a unified way, by using as a main algebraic tool a nonassociative

    更新日期:2020-08-26
  • LOCAL FORMULAS FOR MULTIPLICATIVE FORMS
    Transform. Groups (IF 0.75) Pub Date : 2020-08-15
    A. CABRERA, I. MĂRCUŢ, M. A. SALAZAR

    We provide explicit formulas for integrating multiplicative forms on local Lie groupoids in terms of infinitesimal data. Combined with our previous work [8], which constructs the local Lie groupoid of a Lie algebroid, these formulas produce concrete integrations of several geometric stuctures defined infinitesimally. In particular, we obtain local integrations and non-degenerate realizations of Poisson

    更新日期:2020-08-15
  • ON THE CHARACTERIZATION OF DANIELEWSKI SURFACES BY THEIR AUTOMORPHISM GROUPS
    Transform. Groups (IF 0.75) Pub Date : 2020-08-12
    ALVARO LIENDO, ANDRIY REGETA, CHRISTIAN URECH

    In this note we show that if the automorphism group of a normal affine surface S is isomorphic to the automorphism group of a Danielewski surface, then S is isomorphic to the normalization of a Danielewski surface.

    更新日期:2020-08-12
  • Completing the Classification of Representations of SL n with Complete Intersection Invariant Ring
    Transform. Groups (IF 0.75) Pub Date : 2020-08-11
    LUKAS BRAUN

    We present a full list of all representations of the special linear group SLn over the complex numbers with complete intersection invariant ring of homological dimension greater than or equal to two, completing the classification of Shmelkin. For this task, we combine three techniques. Firstly, the graph method for invariants of SLn developed by the author to compute invariants, covariants and explicit

    更新日期:2020-08-11
  • TWISTED DOLBEAULT COHOMOLOGY OF NILPOTENT LIE ALGEBRAS
    Transform. Groups (IF 0.75) Pub Date : 2020-08-07
    LIVIU ORNEA, MISHA VERBITSKY

    It is well known that the cohomology of any non-trivial 1-dimensional local system on a nilmanifold vanishes (this result, due to J. Dixmier, was also announced and proved in some particular case by Alaniya). A complex nilmanifold is a quotient of a nilpotent Lie group equipped with a left-invariant complex structure by an action of a discrete, co-compact subgroup. We prove a Dolbeault version of Dixmier’s

    更新日期:2020-08-08
  • UNIFORM KAZHDAN CONSTANTS AND PARADOXES OF THE AFFINE PLANE
    Transform. Groups (IF 0.75) Pub Date : 2020-08-06
    LAM L. PHAM

    Let G = SL(2, ℤ) ⋉ ℤ2 and H = SL(2, ℤ). We prove that the action G ↷ ℝ2 is uniformly non-amenable and that the quasi-regular representation of G on ℓ2(G/H) has a uniform spectral gap. Both results are a consequence of a uniform quantitative form of ping-pong for affine transformations, which we establish here.

    更新日期:2020-08-06
  • PSEUDOCHARACTERS OF HOMOMORPHISMS INTO CLASSICAL GROUPS
    Transform. Groups (IF 0.75) Pub Date : 2020-08-06
    M. WEIDNER

    A GLd-pseudocharacter is a function from a group Γ to a ring k satisfying polynomial relations that make it “look like” the character of a representation. When k is an algebraically closed field of characteristic 0, Taylor proved that GLd-pseudocharacters of Γ are the same as degree-d characters of Γ with values in k, hence are in bijection with equivalence classes of semisimple representations Γ →

    更新日期:2020-08-06
  • ON THE RICCI ITERATION FOR HOMOGENEOUS METRICS ON SPHERES AND PROJECTIVE SPACES
    Transform. Groups (IF 0.75) Pub Date : 2020-08-06
    T. BUTTSWORTH, A. PULEMOTOV, Y. A. RUBINSTEIN, W. ZILLER

    We study the Ricci iteration for homogeneous metrics on spheres and complex projective spaces. Such metrics can be described in terms of modifying the canonical metric on the fibers of a Hopf fibration. When the fibers of the Hopf fibration are circles or spheres of dimension 2 or 7, we observe that the Ricci iteration as well as all ancient Ricci iterations can be completely described using known

    更新日期:2020-08-06
  • NON-SOLVABLE LIE GROUPS WITH NEGATIVE RICCI CURVATURE
    Transform. Groups (IF 0.75) Pub Date : 2020-06-16
    EMILIO A. LAURET, CYNTHIA E. WILL

    Until a couple of years ago, the only known examples of Lie groups admitting left-invariant metrics with negative Ricci curvature were either solvable or semisimple.We use a general construction from a previous article of the second named author to produce a large number of examples with compact Levi factor. Given a compact semisimple real Lie algebra 𝔲 and a real representation π satisfying some

    更新日期:2020-08-05
  • GENERICALLY FREE REPRESENTATIONS III: EXTREMELY BAD CHARACTERISTIC
    Transform. Groups (IF 0.75) Pub Date : 2020-07-31
    SKIP GARIBALDI; ROBERT M. GURALNICK

    In parts I and II, we determined which faithful irreducible representations V of a simple linear algebraic group G are generically free for Lie(G), i.e., which V have an open subset consisting of vectors whose stabilizer in Lie(G) is zero, with some assumptions on the characteristic of the field. This paper settles the remaining cases, which are of a different nature because Lie(G) has a more complicated

    更新日期:2020-07-31
  • GENERICALLY FREE REPRESENTATIONS II: IRREDUCIBLE REPRESENTATIONS
    Transform. Groups (IF 0.75) Pub Date : 2020-07-27
    SKIP GARIBALDI; ROBERT M. GURALNICK

    We determine which faithful irreducible representations V of a simple linear algebraic group G are generically free for Lie(G), i.e., which V have an open subset consisting of vectors whose stabilizer in Lie(G) is zero. This relies on bounds on dim V obtained in prior work (part I), which reduce the problem to a finite number of possibilities for G and highest weights for V , but still infinitely many

    更新日期:2020-07-27
  • BRAIDED COMMUTATIVE ALGEBRAS OVER QUANTIZED ENVELOPING ALGEBRAS
    Transform. Groups (IF 0.75) Pub Date : 2020-07-20
    ROBERT LAUGWITZ, CHELSEA WALTON

    We produce braided commutative algebras in braided monoidal categories by generalizing Davydov’s full center construction of commutative algebras in centers of monoidal categories. Namely, we build braided commutative algebras in relative monoidal centers \( {\mathcal{Z}}_{\mathrm{\mathcal{B}}}\left(\mathcal{C}\right) \) from algebras in ℬ-central monoidal categories \( \mathcal{C} \), where ℬ is an

    更新日期:2020-07-20
  • COHOMOLOGICAL INVARIANTS OF THE STACK OF HYPERELLIPTIC CURVES OF ODD GENUS
    Transform. Groups (IF 0.75) Pub Date : 2020-07-18
    A. DI LORENZO

    We compute the cohomological invariants of ℋg, the moduli stack of smooth hyperelliptic curves, for every odd g.

    更新日期:2020-07-18
  • SPHERICAL ACTIONS ON ISOTROPIC FLAG VARIETIES AND RELATED BRANCHING RULES
    Transform. Groups (IF 0.75) Pub Date : 2020-07-13
    ROMAN AVDEEV, ALEXEY PETUKHOV

    Let G be a symplectic or special orthogonal group, let H be a connected reductive subgroup of G, and let X be a flag variety of G. We classify all triples (G, H, X) such that the natural action of H on X is spherical. For each of these triples, we determine the restrictions to H of all irreducible representations of G realized in spaces of sections of homogeneous line bundles on X.

    更新日期:2020-07-13
  • INVARIANT HILBERT SCHEME RESOLUTION OF POPOV’S SL(2)-VARIETIES
    Transform. Groups (IF 0.75) Pub Date : 2020-07-13
    AYAKO KUBOTA

    We show that every 3-dimensional affine normal quasihomogeneous SL(2)-variety has an equivariant resolution of singularities given by an invariant Hilbert scheme and we present an explicit description of the invariant Hilbert scheme.

    更新日期:2020-07-13
  • NESTINGS OF RATIONAL HOMOGENEOUS VARIETIES
    Transform. Groups (IF 0.75) Pub Date : 2020-07-13
    ROBERTO MUÑOZ, GIANLUCA OCCHETTA, LUIS E. SOLÁ CONDE

    In this paper we study the existence of sections of universal bundles on rational homogeneous varieties–called nestings–classifying them completely on rational homogeneous varieties G/P in the case where G is a simple group of classical type and P is a parabolic subgroup of G. In particular we show that, under this hypothesis, nestings do not exist unless there exists a proper algebraic subgroup of

    更新日期:2020-07-13
  • GEODESICS ON RIEMANNIAN STACKS
    Transform. Groups (IF 0.75) Pub Date : 2020-07-10
    M. DEL HOYO, M. DE MELO

    Metrics on Lie groupoids and differentiable stacks have been introduced recently, extending the Riemannian geometry of manifolds and orbifolds to more general singular spaces. Here we continue that theory, studying stacky curves on Riemannian stacks, measuring their length using stacky metrics, and introducing stacky geodesics. Our main results show that the length of stacky curves measure distances

    更新日期:2020-07-10
  • ZARISKI’S FINITENESS THEOREM AND PROPERTIES OF SOME RINGS OF INVARIANTS
    Transform. Groups (IF 0.75) Pub Date : 2020-07-10
    R. V. GURJAR, S. R. GURJAR, B. HAJRA

    In this paper we will give a short proof of a special case of Zariski’s result about finite generation in connection with Hilbert’s 14th problem using a new idea. Our result is useful for invariant subrings of unipotent or connected semisimple groups. We will also prove an analogue of Miyanishi’s result for the ring of invariants of a \( {\mathbbm{G}}_a \)-action on R[X, Y, Z] for an affine Dedekind

    更新日期:2020-07-10
  • SYMMETRIC SPACES WITH DISSECTING INVOLUTIONS
    Transform. Groups (IF 0.75) Pub Date : 2020-07-10
    K.-H. NEEB, G. ÓLAFSSON

    An involutive diffeomorphism σ of a connected smooth manifold M is called dissecting if the complement of its fixed point set is not connected. Dissecting involutions on a complete Riemannian manifold are closely related to constructive quantum field theory through the work of Dimock and Jaffe/Ritter on the construction of reflection positive Hilbert spaces. In this article we classify all pairs (M

    更新日期:2020-07-10
  • G a $$ {\mathbbm{G}}_a $$ -ACTIONS ON THE COMPLEMENTS OF HYPERSURFACES
    Transform. Groups (IF 0.75) Pub Date : 2020-07-04
    JIHUN PARK

    Let S be a del Pezzo surface with at worst Du Val singularities such that it is a hypersurface in a weighted projective space ℙ. We prove that the surface S contains a (−KS)-polar cylinder if and only if the automorphism group of the affine variety ℙ \ S contains a unipotent subgroup.

    更新日期:2020-07-05
  • MONOMIAL BASES AND BRANCHING RULES
    Transform. Groups (IF 0.75) Pub Date : 2020-06-27
    ALEXANDER MOLEV, OKSANA YAKIMOVA

    Following a question of Vinberg, a general method to construct monomial bases for finite-dimensional irreducible representations of a reductive Lie algebra \( \mathfrak{g} \) was developed in a series of papers by Feigin, Fourier, and Littelmann. Relying on this method, we construct monomial bases of multiplicity spaces associated with the restriction of the representation to a reductive subalgebra

    更新日期:2020-06-27
  • GENERALIZED ORBITAL VARIETIES FOR MIRKOVIĆ–VYBORNOV SLICES AS AFFINIZATIONS OF MIRKOVIĆ–VILONEN CYCLES
    Transform. Groups (IF 0.75) Pub Date : 2020-06-23
    ANNE DRANOWSKI

    We show that generalized orbital varieties for Mirković–Vybornov slices can be indexed by semi-standard Young tableaux, and, via the Mirković–Vybornov isomorphism [MV19], can be identified with Mirković–Vilonen cycles, such that the (combinatorial) Lusztig datum of a generalized orbital variety, which it inherits from its tableau, is equal to the (geometric) Lusztig datum of its Mirković–Vilonen cycle

    更新日期:2020-06-23
  • ON TOPOLOGICAL PROPERTIES OF POSITIVE COMPLEXITY ONE SPACES
    Transform. Groups (IF 0.75) Pub Date : 2020-06-23
    S. SABATINI, D. SEPE

    Motivated by work of Fine and Panov, and of Lindsay and Panov, we prove that every closed symplectic complexity one space that is positive (e.g., positive monotone) enjoys topological properties that Fano varieties with a complexity one holomorphic torus action possess. In particular, such spaces are simply connected, have Todd genus equal to one and vanishing odd Betti numbers.

    更新日期:2020-06-23
  • LEVEL-ZERO VAN DER KALLEN MODULES AND SPECIALIZATION OF NONSYMMETRIC MACDONALD POLYNOMIALS AT t = ∞
    Transform. Groups (IF 0.75) Pub Date : 2020-06-23
    SATOSHI NAITO, DAISUKE SAGAKI

    Let λ ∈ P+ be a level-zero dominant integral weight, and w the coset representative of minimal length for a coset in W/Wλ, where Wλ is the stabilizer of λ in a finite Weyl group W. In this paper, we give a module \( {\mathbbm{K}}_w^{-}\left(\uplambda \right) \) over the negative part of a quantum affine algebra whose graded character is identical to the specialization at t = ∞ of the nonsymmetric Macdonald

    更新日期:2020-06-23
  • C 1 DEFORMATIONS OF ALMOST GRASSMANNIAN STRUCTURES WITH STRONGLY ESSENTIAL SYMMETRY
    Transform. Groups (IF 0.75) Pub Date : 2020-06-18
    ANDREAS ČAP, KARIN MELNICK

    We construct a family of (2, n)-almost Grassmannian structures of regularity C1, each admitting a one-parameter group of strongly essential automorphisms, and each not flat on any open set containing the higher-order fixed point in its closure. This shows that Theorem 1.3 of [12] does not hold assuming only C1 regularity of the structure (see also [3, Prop. 3.5]).

    更新日期:2020-06-18
  • A SERRE PRESENTATION FOR THE QUANTUM GROUPS
    Transform. Groups (IF 0.75) Pub Date : 2020-06-16
    XINHONG CHEN, MING LU, WEIQIANG WANG

    Let (U, ) be a quasi-split quantum symmetric pair of arbitrary Kac–Moody type, where “quasi-split” means the corresponding Satake diagram contains no black node. We give a presentation of the group with explicit relations. The verification of new relations is reduced to some new q-binomial identities. Consequently, is shown to admit a bar involution under suitable conditions on the parameters.

    更新日期:2020-06-16
  • ON THE BETTI NUMBERS OF SPRINGER FIBERS FOR CLASSICAL TYPES
    Transform. Groups (IF 0.75) Pub Date : 2020-06-16
    DONGKWAN KIM

    For a Weyl group W of classical type, we present a formula to calculate the restriction of (graded) Springer representations of W to a maximal parabolic subgroup W′ where the types of W and W′ are in the same series. As a result, we obtain recursive formulas for the Betti numbers of Springer fibers for classical types.

    更新日期:2020-06-16
  • GEOMETRIC CONSTRUCTION OF QUOTIENTS G / H IN SUPERSYMMETRY
    Transform. Groups (IF 0.75) Pub Date : 2020-06-16
    AKIRA MASUOKA, YUTA TAKAHASHI

    It was proved by the first-named author and Zubkov [13] that given an affine algebraic supergroup \( \mathbbm{G} \) and a closed sub-supergroup ℍ over an arbitrary field of characteristic ≠ 2, the faisceau \( \mathbbm{G}\tilde{/}\mathrm{\mathbb{H}} \) (in the fppf topology) is a superscheme, and is, therefore, the quotient superscheme \( \mathbbm{G}/\mathrm{\mathbb{H}} \), which has some desirable

    更新日期:2020-06-16
  • RANK-FINITENESS FOR G -CROSSED BRAIDED FUSION CATEGORIES
    Transform. Groups (IF 0.75) Pub Date : 2020-06-05
    C. JONES, S. MORRISON, D. NIKSHYCH, E. C. ROWELL

    We establish rank-finiteness for the class of G-crossed braided fusion categories, generalizing the recent result for modular categories and including the important case of braided fusion categories. This necessitates a study of slightly degenerate braided fusion categories and their centers, which are interesting for their own sake.

    更新日期:2020-06-05
  • SIMPLE BOUNDED WEIGHT MODULES OF sl∞,o∞,sp∞$$ \mathfrak{sl}\left(\infty \right),\kern0.5em \mathfrak{o}\left(\infty \right),\kern0.5em \mathfrak{sp}\left(\infty \right) $$
    Transform. Groups (IF 0.75) Pub Date : 2020-06-03
    DIMITAR GRANTCHAROV, IVAN PENKOV

    We classify the simple bounded weight modules of the Lie algebras \( \mathfrak{sl}\left(\infty \right),\kern0.5em \mathfrak{o}\left(\infty \right) \) and \( \mathfrak{sp}\left(\infty \right) \), and compute their annihilators in \( U\left(\mathfrak{sl}\left(\infty \right)\right),\kern0.5em U\left(\mathfrak{o}\left(\infty \right)\right),\kern0.5em U\left(\mathfrak{sp}\left(\infty \right)\right) \),

    更新日期:2020-06-03
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