Related papers: Character sheaves on disconnected groups, V

We begin the study of character sheaves on a not necessarily connected reductive group, extending the known theory for connected groups.

We continue the attempt to develop a theory of character sheaves on a not necessarily connected reductive algebraic group. In this paper we introduce and study the generalized Green functions.

We define the notion of character sheaf on a possibly disconnected reductive group. We show that the restriction functor carries a character sheaf to a direct sum of character sheaves.

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 paper we continue the study of character sheaves on a reductive group G. To each subset of the set of simple reflections in the Weyl group we associate an algebra of the same kind as an Iwahori-Hecke algebra with unequal parameters…

We classify the unipotent character sheaves on a fixed connected component of a reductive algebraic group under a mild hypothesis on the characteristic of the ground field.

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.

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 the first chapters, this paper contains a survey on the theory of ordinary characters of finite reductive groups with non-connected centre. The last chapters are devoted to the proof of Lusztig's conjecture on characteristic functions of…

This paper concerns character sheaves of connected reductive algebraic groups defined over non-Archimedean local fields and their relation with characters of smooth representations. Although character sheaves were devised with characters of…

We associate a two-sided cell to any (parabolic) character sheaf. We study the interaction of the duality operator for character sheaves and the operation of "twisted induction".

We define character varieties with non-connected structure groups of finitely presented discrete groups and study some basic aspects, such as generic conjugacy classes and relation with fixed points in character varieties with connected…

The theory of character sheaves on a reductive group is extended to a class of varieties which includes the strata of the De Concini-Procesi completion of an adjoint group.

This paper is an introduction, in a simplified setting, to Lusztig's theory of character sheaves. It develops a notion of character sheaves on reductive Lie algebras which is more general then such notion of Lusztig, and closer to Lusztig's…

Let G be a possibly disconnected reductive group over a finite field with Frobenius map F. The main result of this paper is that the characteristic functions af "admissible complexes" A on G such that F^*A is isomorphic to A form a basis of…

In the first section we study a functor of Bezrukavnikov, Finkelberg and Ostrik defined on character sheaves; we compute it in a Grothendieck group taking weights into account. In the second section we enlarge the class of character sheaves…

We give a combinatorial description of the dg category of character sheaves on a complex reductive group $G$, extending results of [Li] for $G$ simply-connected. We also explicitly identify the parabolic induction/restriction functors.

Let D be a connected component of a reductive group over an algebraically closed field. We define a surjective map from the unipotent character sheaves on D to the set of strata of D, extending an earlier result which applied to connected…

We prove that character sheaves have nilpotent singular support in any characteristic, partially extending the work of Mirkovic, Vilonen and independently Ginzburg to positive characteristic. We do this by introducing a category of tame…

We give an explicit description of character sheaves for the symmetric pairs associated to inner involutions of the special linear groups. We make use of the general strategy given in [VX1] and central character consideration. We also…