Related papers: Springer basic sets and modular Springer correspon…

In this paper we discuss some of Springer's work on unipotent elements in a reductive groups and on representations of Weyl groups. Among the topics considered are Springer's bijection from the unipotent variety to the nilpotent variety,…

We prove an integral version of the derived Springer correspondence for reduced motives. To achieve this result, we extend some results on reduced motives from schemes to quotient stacks with a finite number of orbits. More generally, we…

In \cite{Lusztig}, Lusztig gives an explicit formula for the bijection between the set of bipartitions and the set $\mathcal{N}$ of unipotent classes in a spin group which carry irreducible local systems equivariant for the spin group but…

Let G be a simple reductive group over the complex numbers. Let W be the Weyl group of G. We propose a description of the Springer representations of W associated to various unipotent classes of G by a purely algebraic method involving the…

We give explicit formulas on total Springer representations for classical types. We also describe the characters of restrictions of such representations to a maximal parabolic subgroup isomorphic to a symmetric group. As a result, we give…

We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…

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,…

This is not standard in the sense that we understand a Springer map to be a collapsing of homogeneous bundles. Apart from that we use mostly techniques from Chriss and Ginzbergs book but we work in the equivariant derived category of…

For a Weyl group W, we give a simple closed formula (valid on elliptic conjugacy classes) for the character of the representation of W in each A-isotypic component of the full homology of a Springer fiber. We also give a formula (valid…

A parametrization of irreducible representations associated with a regular adjoint orbit of a classical group over finite quotient rings of the ring of integer of a non-dyadic non-archimedean local field is presented. The parametrization is…

We give an apriori description of a set of irreducible representations of a Weyl group which parametrize the nilpotent orbits in the Lie algebra of a connected reductive group in arbitrary characteristic. We also answer a question of Serre…

We establish a Bruhat decomposition indexed by the wreath product $\Sigma_m\wr \Sigma_d$ between two symmetric groups -- note that $\Sigma_m\wr \Sigma_d$ is not a Coxeter group in general. We show that such a decomposition affords a…

We study the notion of essential dimension for a linear representation of a finite group. In characteristic zero we relate it to the canonical dimension of certain products of Weil transfers of generalized Severi-Brauer varieties. We then…

We use the Springer correspondence to give a partial characterization of the irreducible representations which appear in the Tymoczko dot-action of the Weyl group on the cohomology ring of a regular semisimple Hessenberg variety. In type A,…

We introduce an elliptic version of the Grothendieck-Springer sheaf and establish elliptic analogues of the basic results of Springer theory. From a geometric perspective, our constructions specialize geometric Eisenstein series to the…

The Schur orthogonality relations are a cornerstone in the representation theory of groups. We utilize a generalization to weak Hopf algebras to provide a new, readily verifiable condition on the skeletal data for deciding whether a given…

Let g be a complex semisimple Lie algebra, and f : g --> g/G the adjoint quotient map. Springer theory of Weyl group representations can be seen as the study of the singularities of f. We give a generalization of Springer theory to visible,…

The representation theory of semisimple algebraic groups over the complex numbers (equivalently, semisimple complex Lie algebras or Lie groups, or real compact Lie groups) and the question of whether a given representation is symplectic or…

We construct a new family of homomorphisms from Specht modules into Foulkes modules for the symmetric group. These homomorphisms are used to give a combinatorial description of the minimal partitions (in the dominance order) which label…

The main purpose of this article is to supplement the authors' results on degenerate principal series representations of real symplectic groups with the analogous results for metaplectic groups. The basic theme, as in the previous case, is…