Related papers: Character sheaves for symmetric pairs: special lin…
We determine character sheaves for symmetric pairs associated to spin groups. In particular, we determine the cupsidal character sheaves and show that they can be obtained via the nearby cycle construction of [GVX] and its generalisation in…
We establish a Springer theory for classical symmetric pairs. We give an explicit description of character sheaves in this setting. In particular we determine the cuspidal character sheaves.
In this paper we introduce a new ingredient, invariant systems of differential equations, to our study of character sheaves on graded Lie algebras. The character sheaves we construct in this paper, together with the ones constructed in…
This paper contains an exposition of the theory of character sheaves for reductive groups and some attempts to extend it to other cases: unipotent groups, reductive groups modulo the unipotent radical of a parabolic.
In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg's type II classical graded Lie algebras.
We define and study convolution of parabolic character sheaves. As an application we attach to any parabolic character sheaf the orbit of a tame local system on the maximal torus under a subgroup of the Weyl group.
In this paper we construct full support character sheaves for stably graded Lie algebras. Conjecturally these are precisely the cuspidal character sheaves. Irreducible representations of Hecke algebras associated to complex reflection…
We discuss various computational issues around the problem of determining the character values of finite Chevalley groups, in the framework provided by Lusztig's theory of character sheaves. Some of the remaining open questions (concerning…
In this paper we give a complete classification of cyclically graded semisimple Lie algebras that afford cuspidal character sheaves and determine the support of the cuspidal character sheaves. This constitutes a major step towards the…
Let X be an exotic symmetric space G/H \times V, where G= GL(V) and H = Sp(V) for a symplectic vector space V over an algebraically closed field of odd characteristic. In our previous papers, character sheaves on X were constructed based on…
We determine cuspidal character sheaves explicitly for all (GIT) stably graded exceptional Lie algebras.
In the first part, we construct a new isomorphism between the endomorphism algebra of an induced cuspidal character sheaf and the group algebra of the relative Weyl group involved. We show it differs from the isomorphism of Lusztig by a…
In this paper, we determine the diameter of the commuting involution graphs of special and general linear groups over an arbitrary field. It turns out that our results also determine the diameter for certain projective special linear groups…
We give classifications of linear orbits of pairs of square matrices with non-vanishing discriminant polynomials over a field in terms of certain coherent sheaves with additional data on closed subschemes of the projective line. Our results…
We continue the study of character sheaves on a not necessarily connected reductive group. We prove orthogonality formulas for certain characteristic functions.
We begin the study of character sheaves on a not necessarily connected reductive group, extending the known theory for connected groups.
We relate a generic character sheaf on a disconnected reductive group with a character of a representation of the rational points of the group over a finite field extending a result known in the connected case.
In this article we formulate and prove the main theorems of the theory of character sheaves on unipotent groups over an algebraically closed field of characteristic p>0. In particular, we show that every admissible pair for such a group G…
We show that some types for supercuspidal representations of tamely ramified $p$-adic groups that appear in Jiu-Kang Yu's work are geometrizable. To do so, we define a function-sheaf dictionary for one-dimensional characters of arbitrary…
In this paper, we prove Lusztig's conjecture for finite special linear groups, i.e., we show that characteristic functions of character sheaves coincide with almost characters up to scalar constants, under the condition that the…