Related papers: A classification of spherical conjugacy classes

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.

For a finite group $G,$ we define the concept of $G$-partial permutation and use it to show that the structure coefficients of the center of the wreath product $G\wr \mathcal{S}_n$ algebra are polynomials in $n$ with non-negative integer…

We give a complete classification of the reductive symmetric pairs (G,H) for which the homogeneous space $(G \times H)/diag(H)$ is real spherical in the sense that a minimal parabolic subgroup has an open orbit. Combining with a criterion…

The problem of finding a canonical form of complex matrices up to conjugacy with the set of canonical matrices being a union of affine planes in the matrix space is considered. A solution of the problem is given producing a new canonical…

We classify simple finite Jordan conformal superalgebras and establish preliminary results for the classification of simple finite Jordan pseudoalgebras.

We prove the Arad-Herzog conjecture for various families of finite simple groups- if A and B are nontrivial conjugacy classes, then AB is not a conjugacy class. We also prove that if G is a finite simple group of Lie type and A and B are…

We classify group gradings on the simple Lie algebras of types $G_2$ and $D_4$ over the field of real numbers (or any real closed field): fine gradings up to equivalence and $G$-gradings, with a fixed group $G$, up to isomorphism.

We obtain several structure results for a class of spherical subgroups of connected reductive complex algebraic groups that extends the class of strongly solvable spherical subgroups. Based on these results, we construct certain…

We define the spherical Hecke algebra for an (untwisted) affine Kac-Moody group over a local non-archimedian field. We prove a generalization of the Satake isomorphism for these algebras, relating it to integrable representations of the…

We show that the weighted fusion category algebra of the principal 2-block $b_0$ of $\mathrm{GL}_2(q)$ is the quotient of the $q$-Schur algebra $\mathcal{S}_2(q)$ by its socle, for $q$ an odd prime power. As a consequence, we get a…

Given an exceptional simple complex algebraic group G and a symmetric pair (G, K), we study the spherical nilpotent K-orbit closures in the isotropy representation of K. We show that they are all normal except in one case in type G2, and…

In this paper, we study the structure of finite groups with a large number of conjugacy classes of $p$-elements for some prime $p$. As consequences, we obtain some new criteria for the existence of normal $p$-complements in finite groups.

Let H be a spherical subgroup of minimal rank of the semisimple simply connected complex algebraic group G. We define some functions on the homogeneous space G/H that we call generalised spherical minors. When G = H x H, we recover…

We categorify one half of the small quantum sl(2) at a prime root of unity. An extension of this construction to an arbitrary simply-laced case is proposed.

The right conjugacy closed loops of order 2p, where p is an odd prime, are classified up to isomorphism.

We express the set of representations from a cyclic $p$-group to a connected $p$-compact group in terms of the associated reflection group and compute its cardinality for each exotic $p$-compact group.

We prove a myriad of results related to the stabilizer in an algebraic group $G$ of a generic vector in a representation $V$ of $G$ over an algebraically closed field $k$. Our results are on the level of group schemes, which carries more…

We first describe, over a field K of characteristic different from 2, the orbits for the adjoint actions of the Lie groups PGL(2, K) and PSL(2, K) on their Lie algebra sl(2, K). While the former are well known, the latter lead to the…

We classify all division algebras that are principal Albert isotopes of a cyclic Galois field extension of degree $n>2$ up to isomorphisms. We achieve a ``tight'' classification when the cyclic Galois field extension is cubic. The…

We define noncommutative deformations $W_q^s(G)$ of algebras of functions on certain (finite coverings of) transversal slices to the set of conjugacy classes in an algebraic group $G$ which play the role of Slodowy slices in algebraic group…