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  • 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
  • A COMBINATORIAL FORMULA FOR GRADED MULTIPLICITIES IN EXCELLENT FILTRATIONS
    Transform. Groups (IF 0.75) Pub Date : 2020-05-22
    REKHA BISWAL, DENIZ KUS

    A filtration of a representation whose successive quotients are isomorphic to Demazure modules is called an excellent filtration. In this paper we study graded multiplicities in excellent filtrations of fusion products for the current algebra \( {\mathfrak{sl}}_2\left[t\right] \). We give a combinatorial formula for the polynomials encoding these multiplicities in terms of two-dimensional lattice paths

    更新日期:2020-05-22
  • THE PBW THEOREM FOR AFFINE YANGIANS
    Transform. Groups (IF 0.75) Pub Date : 2020-05-22
    YAPING YANG, GUFANG ZHAO

    We prove that the Yangian associated to an untwisted symmetric affine Kac–Moody Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter is constructed in [YZ14] as an algebraic formalism of cohomological Hall algebras. As a consequence, we obtain the Poincare–Birkhoff–Witt (PBW) theorem for this class of affine Yangians. Another independent proof of the PBW theorem is given

    更新日期:2020-05-22
  • GENERALISED GELFAND–GRAEV REPRESENTATIONS IN BAD CHARACTERISTIC ?
    Transform. Groups (IF 0.75) Pub Date : 2020-05-22
    MEINOLF GECK

    Let G be a connected reductive algebraic group defined over a finite field with q elements. In the 1980’s, Kawanaka introduced generalised Gelfand–Graev representations of the finite group \( G\left({\mathbbm{F}}_q\right) \), assuming that q is a power of a good prime for G. These representations have turned out to be extremely useful in various contexts. Here we investigate to what extent Kawanaka’s

    更新日期:2020-05-22
  • THE EXCEPTIONAL TITS QUADRANGLES
    Transform. Groups (IF 0.75) Pub Date : 2020-05-22
    BERNHARD MÜHLHERR, RICHARD M. WEISS

    A Tits polygon is a bipartite graph in which the neighborhood of each vertex is endowed with an “opposition relation” satisfying certain axioms. Moufang polygons are precisely the Tits polygons in which these opposition relations are all trivial. Every Tits polygon has a distinguished set of circuits. A Tits quadrangle is a Tits polygon in which these circuits all have length 8. There is a standard

    更新日期:2020-05-22
  • INERTIA GROUPS AND UNIQUENESS OF HOLOMORPHIC VERTEX OPERATOR ALGEBRAS
    Transform. Groups (IF 0.75) Pub Date : 2020-05-21
    CHING HUNG LAM, HIROKI SHIMAKURA

    We continue our program on classiffication of holomorphic vertex operator algebras of central charge 24. In this article, we show that there exists a unique strongly regular holomorphic VOA of central charge 24, up to isomorphism, if its weight one Lie algebra has the type C4,10, D7,3A3,1G2,1, A5,6C2,3A1,2, A3,1C7,2, D5,4C3,2A\( {A}_{1,1}^2 \), or E6,4C2,1A2,1. As a consequence, we have verified that

    更新日期:2020-05-21
  • BOUNDEDNESS PROPERTIES OF AUTOMORPHISM GROUPS OF FORMS OF FLAG VARIETIES
    Transform. Groups (IF 0.75) Pub Date : 2020-05-16
    A. GULD

    We call a flag variety admissible if its automorphism group is the projective general linear group. (This holds in most cases.) Let K be a field of characteristic 0, containing all roots of unity. Let the K-variety X be a form of an admissible flag variety. We prove that X is either ruled, or the automorphism group of X is bounded, meaning that there exists a constant C ∈ ℕ such that if G is a finite

    更新日期:2020-05-16
  • SEMISIMPLE CYCLIC ELEMENTS IN SEMISIMPLE LIE ALGEBRAS
    Transform. Groups (IF 0.75) Pub Date : 2020-05-04
    A. G. ELASHVILI, M. JIBLADZE, V. G. KAC

    This paper is a continuation of the theory of cyclic elements in semisimple Lie algebras, developed by Elashvili, Kac and Vinberg. Its main result is the classification of semisimple cyclic elements in semisimple Lie algebras. The importance of this classification stems from the fact that each such element gives rise to an integrable hierarchy of Hamiltonian PDE of Drinfeld–Sokolov type.

    更新日期:2020-05-04
  • SHEAVES ON THE ALCOVES AND MODULAR REPRESENTATIONS I
    Transform. Groups (IF 0.75) Pub Date : 2020-05-04
    P. FIEBIG, M. LANINI

    We consider the set of affine alcoves associated with a root system R as a topological space and define a certain category S of sheaves of \( {\mathcal{Z}}_k \)-modules on this space. Here \( {\mathcal{Z}}_k \) is the structure algebra of the root system over a field k. To any wall reection s we associate a wall crossing functor on S. In the companion article [FL] we prove that S encodes the simple

    更新日期:2020-05-04
  • LAGRANGIAN FIBERS OF GELFAND–CETLIN SYSTEMS OF SO( n )-TYPE
    Transform. Groups (IF 0.75) Pub Date : 2020-05-04
    YUNHYUNG CHO, YOOSIK KIM

    In this paper, we study the Gelfand–Cetlin systems and polytopes of the co-adjoint SO(n)-orbits. We describe the face structure of Gelfand–Cetlin polytopes and iterated bundle structure of Gelfand–Cetlin fibers in terms of combinatorics on the ladder diagrams. Using this description, we classify all Lagrangian fibers.

    更新日期:2020-05-04
  • ADMISSIBLE LEVEL osp12$$ \mathfrak{osp}\left(1\left|2\right.\right) $$ MINIMAL MODELS AND THEIR RELAXED HIGHEST WEIGHT MODULES
    Transform. Groups (IF 0.75) Pub Date : 2020-05-04
    SIMON WOOD

    The minimal model \( \mathfrak{osp}\left(1|2\right) \) vertex operator superalgebras are the simple quotients of affine vertex operator superalgebras constructed from the affine Lie super algebra \( \hat{\mathfrak{osp}}\left(1\left|2\right.\right) \) at certain rational values of the level k. We classify all isomorphism classes of ℤ2-graded simple relaxed highest weight modules over the minimal model

    更新日期:2020-05-04
  • Correction to: STRATIFIED HYPERKÄHLER SPACES FROM SEMISIMPLE LIE ALGEBRAS
    Transform. Groups (IF 0.75) Pub Date : 2020-04-29
    MAXENCE MAYRAND

    This erratum concerns the Kähler potential F defined in the second displayed equation of [M, Sect. 4.2], which is incorrectly claimed to be proper.

    更新日期:2020-04-29
  • SHEAVES ON THE ALCOVES AND MODULAR REPRESENTATIONS II
    Transform. Groups (IF 0.75) Pub Date : 2020-04-29
    P. FIEBIG, M. LANINI

    We relate the category of sheaves on alcoves that was constructed in [FL1] to the representation theory of reductive algebraic groups. In particular, we show that its indecomposable projective objects encode the irreducible rational characters of a connected, semisimple and simply connected reductive algebraic group for characteristics above the Coxeter number.

    更新日期:2020-04-29
  • AUSLANDER’S THEOREM FOR GROUP COACTIONS ON NOETHERIAN GRADED DOWN-UP ALGEBRAS
    Transform. Groups (IF 0.75) Pub Date : 2020-04-29
    J. CHEN, E. KIRKMAN, J. J. ZHANG

    We prove a version of a theorem of Auslander for finite group coactions on noetherian graded down-up algebras.

    更新日期:2020-04-29
  • CONFORMAL PROPERTIES OF INDEFINITE BI-INVARIANT METRICS
    Transform. Groups (IF 0.75) Pub Date : 2020-04-29
    KELLI FRANCIS-STAITE, THOMAS LEISTNER

    An indecomposable Lie group with Riemannian bi-invariant metric is always simple and hence Einstein. Indefinite bi-invariant metrics are not necessarily Einstein, not even on simple Lie groups. We study the question of whether a semi-Riemannian bi-invariant metric is conformal to an Einstein metric. We obtain results for all three cases in the structure theorem by Medina and Revoy for indecomposable

    更新日期:2020-04-29
  • DEGENERATE SCHUBERT VARIETIES IN TYPE A
    Transform. Groups (IF 0.75) Pub Date : 2020-04-14
    ROCCO CHIRIVÌ, XIN FANG, GHISLAIN FOURIER

    We introduce rectangular elements in the symmetric group. In the framework of PBW degenerations, we show that in type A the degenerate Schubert variety associated with a rectangular element is indeed a Schubert variety in a partial ag variety of the same type with larger rank. Moreover, the degenerate Demazure module associated with a rectangular element is isomorphic to the Demazure module for this

    更新日期:2020-04-14
  • HOPF ALGEBRA ACTIONS IN TENSOR CATEGORIES
    Transform. Groups (IF 0.75) Pub Date : 2020-04-14
    M. BISCHOFF, A. DAVYDOV

    We prove that commutative algebras in braided tensor categories do not admit faithful Hopf algebra actions unless they come from group actions. We also show that a group action allows us to see the algebra as the regular algebra in the representation category of the acting group.

    更新日期:2020-04-14
  • WEYL’S POLARIZATION THEOREM IN POSITIVE CHARACTERISTIC
    Transform. Groups (IF 0.75) Pub Date : 2020-04-14
    H. DERKSEN, V. MAKAM

    Let V be an n-dimensional algebraic representation over an algebraically closed field K of a group G. For m > 0, we study the invariant rings K[Vm]G for the diagonal action of G on Vm. In characteristic zero, a theorem of Weyl tells us that we can obtain all the invariants in K[Vm]G by the process of polarization and restitution from K[Vn]G. In particular, this means that if K[Vn]G is generated in

    更新日期:2020-04-14
  • TANNAKIAN CLASSIFICATION OF EQUIVARIANT PRINCIPAL BUNDLES ON TORIC VARIETIES
    Transform. Groups (IF 0.75) Pub Date : 2020-03-21
    INDRANIL BISWAS, ARIJIT DEY, MAINAK PODDAR

    Let X be a complete toric variety equipped with the action of a torus T, and G a reductive algebraic group, defined over an algebraically closed field K. We introduce the notion of a compatible ∑-filtered algebra associated to X, generalizing the notion of a compatible ∑-filtered vector space due to Klyachko, where ∑ denotes the fan of X. We combine Klyachko's classification of T-equivariant vector

    更新日期:2020-03-21
  • BRAID GROUP ACTION AND ROOT VECTORS FOR THE q -ONSAGER ALGEBRA
    Transform. Groups (IF 0.75) Pub Date : 2020-03-07
    PASCAL BASEILHAC, STEFAN KOLB

    We define two algebra automorphisms Ͳ0 and Ͳ1 of the q-Onsager algebra \( {\mathcal{B}}_c \), which provide an analog of G. Lusztig's braid group action for quantum groups. These automorphisms are used to define root vectors which give rise to a PBW basis for \( {\mathcal{B}}_c \). We show that the root vectors satisfy q-analogs of Onsager's original commutation relations. The paper is much inspired

    更新日期:2020-03-07
  • CLASSIFICATION OF HOMOGENEOUS EINSTEIN METRICS ON PSEUDO-HYPERBOLIC SPACES
    Transform. Groups (IF 0.75) Pub Date : 2020-03-05
    GABRIEL BĂDIŢOIU

    We classify the effective and transitive actions of a Lie group G on an n-dimensional non-degenerate hyperboloid (also called real pseudo-hyperbolic space), under the assumption that G is a closed, connected Lie subgroup of SO0(n–r; r+1), the connected component of the indefinite special orthogonal group. Assuming additionally that G acts completely reducibly on ℝ n +1 , we also obtain that any G-homogeneous

    更新日期:2020-03-05
  • GEOMETRY OF REGULAR HESSENBERG VARIETIES
    Transform. Groups (IF 0.75) Pub Date : 2020-03-03
    HIRAKU ABE, NAOKI FUJITA, HAOZHI ZENG

    Let \( \mathfrak{g} \) be a complex semisimple Lie algebra. For a regular element x in \( \mathfrak{g} \) and a Hessenberg space H ⊆ \( \mathfrak{g} \), we consider a regular Hessenberg variety X(x, H) in the ag variety associated with \( \mathfrak{g} \). We take a Hessenberg space so that X(x, H) is irreducible, and show that the higher cohomology groups of the structure sheaf of X(x, H) vanish. We

    更新日期:2020-03-03
  • NON-STANDARD VERMA TYPE MODULES FOR 𝔮( n ) (2)
    Transform. Groups (IF 0.75) Pub Date : 2020-02-13
    L. CALIXTO, V. FUTORNY

    We study non-standard Verma type modules over the Kac-Moody queer Lie superalgebra 𝔮(n)(2). We give a sufficient condition under which such modules are irreducible. We also give a classification of all irreducible diagonal ℤ-graded modules over certain Heisenberg Lie superalgebras contained in 𝔮(n)(2).

    更新日期:2020-02-13
  • TOWARDS AN INTERSECTION CHOW COHOMOLOGY THEORY FOR GIT QUOTIENTS
    Transform. Groups (IF 0.75) Pub Date : 2020-02-13
    DAN EDIDIN, MATTHEW SATRIANO

    We study the Fulton-MacPherson operational Chow rings of good moduli spaces of properly stable, smooth, Artin stacks. Such spaces are étale locally isomorphic to geometric invariant theory quotients of affine schemes, and are therefore natural extensions of GIT quotients. Our main result is that, with ℚ-coefficients, every operational class can be represented by a topologically strong cycle on the

    更新日期:2020-02-13
  • INDEFINITE HYPERKÄHLER METRICS ON LIE GROUPS WITH ABELIAN COMPLEX STRUCTURES
    Transform. Groups (IF 0.75) Pub Date : 2020-02-13
    IGNACIO BAJO, ESPERANZA SANMARTÍN

    We consider Lie groups G endowed with a pair of anticommuting left-invariant abelian complex structures (J1, J2) and a left-invariant (possibly indefinite) metric g such that (G, J1, J2, g) results to be a hyperkähler manifold. We give a classification of their Lie algebras up to dimension 12 and study some of their geometric properties. In particular, we show that all such groups are locally symmetric

    更新日期:2020-02-13
  • EXTENSIONS OF ISOMORPHISMS OF SUBVARIETIES IN FLEXIBLE VARIETIES
    Transform. Groups (IF 0.75) Pub Date : 2019-12-12
    SHULIM KALIMAN

    Let X be an algebraic variety isomorphic to the complement of a closed subvariety of dimension at most n − 3 in \( {\mathbbm{A}}_{\mathrm{k}}^n \). We find some conditions under which an isomorphism of two closed subvarieties of X can be extended to an automorphism of X. We also study the similar problem for subvarieties of affine quadrics and SL(n, k).

    更新日期:2019-12-12
  • TORUS ACTIONS, LOCALIZATION AND INDUCED REPRESENTATIONS ON COHOMOLOGY
    Transform. Groups (IF 0.75) Pub Date : 2019-08-02
    J. B. CARRELL

    This note is motivated by the problem of understanding Springer’s remarkable representation of the Weyl group W of a semisimple complex linear algebraic group G on the cohomology algebra of an arbitrary Springer variety in the ag variety of G from the viewpoint of torus actions and localization. Continuing the work [CK] which gave a sufficient condition for a group \( \mathcal{W} \) acting on the fixed

    更新日期:2019-08-02
  • AUTOMATIC CONTINUITY OF ABSTRACT HOMOMORPHISMS BETWEEN LOCALLY COMPACT AND POLISH GROUPS
    Transform. Groups (IF 0.75) Pub Date : 2019-07-08
    O. BRAUN, KARL H. HOFMANN, L. KRAMER

    We prove results about automatic continuity and openness of abstract surjective group homomorphisms \( K\overset{\varphi }{\to }G, \) where G and K belong to a certain class К of topological groups, and where the kernel of φ satisies a certain topological countability condition. Our results apply in particular to the case where G is a semisimple Lie group or a semisimple compact group, and where К

    更新日期:2019-07-08
  • THE STRUCTURE OF Q-W ALGEBRAS
    Transform. Groups (IF 0.75) Pub Date : 2019-05-11
    A. SEVOSTYANOV

    We suggest two explicit descriptions of the Poisson q-W algebras which are Poisson algebras of regular functions on certain algebraic group analogues of the Slodowy transversal slices to adjoint orbits in a complex semisimple Lie algebra \( \mathfrak{g} \). To obtain the first description we introduce certain projection operators which are analogous to the quasi-classical versions of the so-called

    更新日期:2019-05-11
  • TAKIFF ALGEBRAS WITH POLYNOMIAL RINGS OF SYMMETRIC INVARIANTS
    Transform. Groups (IF 0.75) Pub Date : 2019-05-03
    DMITRI I. PANYUSHEV, OKSANA S. YAKIMOVA

    Extending results of Rais–Tauvel, Macedo–Savage, and Arakawa–Premet, we prove that under mild restrictions on the Lie algebra \( \mathfrak{q} \) having the polynomial ring of symmetric invariants, the m-th Takiff algebra of \( \mathfrak{q} \), \( \mathfrak{q} \)⟨m⟩, also has a polynomial ring of symmetric invariants.

    更新日期:2019-05-03
  • EQUIVARIANT MODELS OF SPHERICAL VARIETIES
    Transform. Groups (IF 0.75) Pub Date : 2019-04-29
    MIKHAIL BOROVOI

    Let G be a connected semisimple group over an algebraically closed field k of characteristic 0. Let Y = G/H be a spherical homogeneous space of G, and let Y′ be a spherical embedding of Y. Let k0 be a subfield of k. Let G0 be a k0-model (k0-form) of G. We show that if G0 is an inner form of a split group and if the subgroup H of G is spherically closed, then Y admits a G0-equivariant k0-model. If we

    更新日期:2019-04-29
  • NEW BOUNDS ON THE TORAL RANK WITH APPLICATIONS TO COHOMOLOGICALLY SYMPLECTIC SPACES
    Transform. Groups (IF 0.75) Pub Date : 2019-04-22
    L. ZOLLER

    We use Boij–Söderberg theory to give two lower bounds for the dimension of the cohomology of a finite CW-complex in terms of the toral rank and certain Betti numbers of the space. One of our bounds turns out to be particularly effective for c-symplectic spaces, proving the toral rank conjecture for c-symplectic spaces of formal dimension ≤ 8.

    更新日期:2019-04-22
  • DECOMPOSITIONS OF BERNSTEIN–SATO POLYNOMIALS AND SLICES
    Transform. Groups (IF 0.75) Pub Date : 2019-04-17
    ANDRÁS CRISTIAN LŐRINCZ

    Let G be a linearly reductive group acting on a vector space V, and f a semi-invariant polynomial on V. In this paper we study systematically decompositions of the Bernstein–Sato polynomial of f in parallel with some representation-theoretic properties of the action of G on V. We provide a technique based on a multiplicity one property, that we use to compute the Bernstein–Sato polynomials of several

    更新日期:2019-04-17
  • SEIDEL’S CONJECTURES IN HYPERBOLIC 3-SPACE
    Transform. Groups (IF 0.75) Pub Date : 2019-04-17
    OMAR CHAVEZ CUSSY, CARLOS H. GROSSI

    We prove, in the case of hyperbolic 3-space, a couple of conjectures raised by J. J. Seidel in On the volume of a hyperbolic simplex, Stud. Sci. Math. Hung. 21 (1986), 243–249. Seidel’s first conjecture states that the volume of an ideal tetrahedron in hyperbolic 3-space is determined by (the permanent and the determinant of) a certain Gram matrix G of its vertices; Seidel’s fourth conjecture claims

    更新日期:2019-04-17
  • GRADED SUPER DUALITY FOR GENERAL LINEAR LIE SUPERALGEBRAS
    Transform. Groups (IF 0.75) Pub Date : 2019-04-11
    C. LEONARD

    We provide a new proof of the super duality equivalence between infinite-rank parabolic BGG categories of general linear Lie (super) algebras conjectured by Cheng and Wang and first proved by Cheng and Lam. We do this by establishing a new uniqueness theorem for tensor product categorifications motivated by work of Brundan, Losev, and Webster. Moreover we show that these BGG categories have Koszul

    更新日期:2019-04-11
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