Related papers: A classification of spherical conjugacy classes in…

We classify singular foliations admitting a given leaf and a given transverse singular foliation.

We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.

We classify the finite groups $G$ which satisfies the condition that every complex irreducible character,whose degree's square doesn't divide the index of its kernel in $G$, lies in the same Galois conjugacy class.

We reduce the classification of finite subgroups in compact Lie groups to that of quasi-simple ones, prove the number of conjugacy classes is finite and each cojugacy class is Zariski closed in mapping space, and classify "strongly…

We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subcategory, in which the object is spherical. This general…

In this short note, we classify pairs of conjugacy classes of the symmetric group such that any non-linear irreducible character of the symmetric group vanishes on at least one of them.

We classify gradings on matrix algebras by a finite abelian group. A grading is called good if all elementary matrices are homogeneous. For cyclic groups, all gradings on a matrix algebra over an algebraically closed field are good. We can…

Let G' be a connected reductive group over the complex numbers. We show that the set of conjugacy classes of G' is in natural bijection with the set of two-sided cells associated to a certain algebra.

We show that the sheets for a connected reductive algebraic group G over an algebraically closed field in good characteristic acting on itself by conjugation are in bijection with G-conjugacy classes of triples (M, Z(M)^\circ t, O) where M…

Let $G$ be a group. Two elements $x,y \in G$ are said to be in the same $z$-class if their centralizers in $G$ are conjugate within $G$. Consider $\mathbb F$ a perfect field of characteristic $\neq 2$, which has a non-trivial Galois…

In this paper we study Cartan subalgebras in general and special linear algebras over a field of positive characteristic. We determined the conjugacy classes of Cartan subalgebras under the general linear groups, and count the explicit…

We prove that any fusion category over $\mathbb{C}$ with exactly one non-invertible simple object is spherical. Furthermore, we classify all such categories that come equipped with a braiding.

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…

Let $G$ be a connected semisimple algebraic group over an algebraically closed field of characteristic zero, and let $\th$ be an automorphism of $G$. We give a characterization of $\th$-twisted spherical conjugacy classes in $G$ by a…

Many results have been established that show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper is to show several results about solvability concerning the…

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.

We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.

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

We determine the conjugacy classes of semisimple elements in the symplectic groups ${\rm Sp}(2m,F)$, where $F$ is an arbitrary field of characteristic not $2$. This note was originally a letter dated 23 March, 2006, from G.E. Wall to Cheryl…

We classify tame block algebras of Hecke algebras of classical type over an algebraically closed field of odd characteristic.