• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• Transform. Groups (IF 0.75) Pub Date : 2019-12-16
P. BELKALE, J. KIERS

The Hermitian eigenvalue problem asks for the possible eigenvalues of a sum of Hermitian matrices given the eigenvalues of the summands. This is a problem about the Lie algebra of the maximal compact subgroup of G = SL(n). There is a polyhedral cone (the \eigencone") determining the possible answers to the problem. These eigencones can be defined for arbitrary semisimple groups G, and also control

更新日期：2019-12-16
• 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
• Transform. Groups (IF 0.75) Pub Date : 2019-08-02
HOLLEY FRIEDLANDER, WILLIAM GRODZICKI, WAYNE JOHNSON, GAIL RATCLIFF, ANNA ROMANOV, BENJAMIN STRASSER, BRENT WESSEL

Let N be a connected and simply connected nilpotent Lie group, and let K be a subgroup of the automorphism group of N. We say that the pair (K, N) is a nilpotent Gelfand pair if $${L}_K^1(N)$$ is an abelian algebra under convolution. In this document we establish a geometric model for the Gelfand spectra of nilpotent Gelfand pairs (K, N) where the K-orbits in the center of N have a one-parameter

更新日期：2019-08-02
• 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
• 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
• 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
• 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
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