Related papers: Towards the Green correspondence for supergroups

For a prime p and natural number n with p greater than or equal to n, we establish the existence of a non-functorial one-to-one correspondence between isomorphism classes of groups of order p^n whose derived subgroup has exponent dividing…

A general Mackey type decomposition for representations of semisimple Hopf algebras is investigated. We show that such a decomposition occurs in the case that the module is induced from an arbitrary Hopf subalgebra and it is restricted back…

Associated to a composition of M and a composition of N, a new presentation of the super Yangian of the general linear Lie superalgebra $Y(gl_{M|N})$ is obtained.

We discuss progress towards the classification of irreducible admissible representations of reductive groups over non-archimedean local fields and the local Langlands correspondence. We also state some (partly conjectural) compatibility…

Selfdual representations of any group fall into two classes when they are irreducible: those which carry a symmetric bilinear form, and the others which carry an alternating bilinear form. The Langlands correspondence, which matches the…

Let W be a Weyl group. We define a class of irreducible representations of W that we call antispecial. They are in bijection with the constructible representations of W. We define an oriented graph structure on the set of antispecial…

For a group $G$ acting over a set $X$, the set of all the $G$-equivariant functions, i.e., the set of functions which conmute with the action, ($g\cdot f(x)=g\cdot f(x), \forall g\in G, \forall x\in X$), is a monoid with the composition.…

We define a subgroup of the universal sofic group, obtained as the normaliser of a separable abelian subalgebra. This subgroup can be obtained as an extension by the group of automorphisms on a standard probability space. We show that each…

We study the exceptional theta correspondence for real groups obtained by restricting the minimal representation of the split exceptional group of the type E_n, to a split dual pair where one member is the exceptional group of the type G_2.…

In this paper we describe the Greens relations on the semigroup of bi-ideals of ordered full transformation semigroup in terms of Greens relations of ordered full transformation semigroup on a set.

Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to…

We define a generalized Springer correspondence for the group GL(n) over any field. We also determine the cuspidal pairs, and compute the correspondence explicitly. Finally we define a stratification of the category of equivariant perverse…

This is the final draft, containing very minor proof-reading corrections. Let G in SL(n,\C) be a finite subgroup and \fie: Y -> X = \C^n/G any resolution of singularities of the quotient space. We prove that crepant exceptional prime…

The geometric Langlands correspondence for function fields over finite fields has been proved by Frenkel, Gaitsgory, Vilonen. The aim of this article is to write translation for curves over the complex field and prove the correspondence in…

The representation category $\mathcal{A} = Rep(G,\epsilon)$ of a supergroup scheme $G$ has a largest proper tensor ideal, the ideal $\mathcal{N}$ of negligible morphisms. If we divide $\mathcal{A}$ by $\mathcal{N}$ we get the semisimple…

The general structure of the representation theory of a $Z_2$-graded coalgebra is discussed. The result contains the structure of Fourier analysis on compact supergroups and quantisations thereof as a special case. The general linear…

A collection C of subgroups of a finite group G can give rise to three different standard formulas for the cohomology of G in terms of either: the subgroups in C; or their centralizers; or their normalizers. We give a short but systematic…

The algorithm of computing generalized Green functions of a finite reductive group contains some unkonwn scalars occuring from the F_q structure of irreducible local systems on unipotent classes on G. In this paper, we determine such…

Let $F$ be a non-Archimedean local field. Let $\Cal W_F$ be the Weil group of $F$ and $\Cal P_F$ the wild inertia subgroup of $\scr W_F$. Let $\hat{\Cal W}_F$ be the set of equivalence classes of irreducible smooth representations of $\Cal…

Suppose that the finite group $G=AB$ is a mutually permutable product of two subgroups $A$ and $B$. By using Sylow numbers of $A$ and $B$, we present some new bounds of the $p$-length $l_p(G)$ of a $p$-solvable group $G$ and the nilpotent…