Related papers: Character sheaves on disconnected groups, X

Let G be a reductive connected group over the algebraic closure of a finite field. In this paper we give the classification of character sheaves on G in categorical terms (as a categorical centre). Previously such a classification was known…

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.

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

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 continue the study of character sheaves on a not necessarily connected reductive group. We prove orthogonality formulas for certain characteristic functions.

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…

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.

Let A be a character sheaf on a reductive connected group G over an algebraically closed field. Assuming that the characteristic is not bad, we show that for certain conjugacy classes D in G the restriction of A to D is a local system up to…

Let H be a connected reductive group over an algebraically closed field. We define a surjective map from the set CS(H) of unipotent character sheaves on H (up to isomorphism) to the set of strata of H. To do this we use the generalized…

We prove a microlocal characterisation of character sheaves on a reductive Lie algebra over an algebraically closed field of sufficiently large positive characteristic: a perverse irreducible G-equivariant sheaf is a character sheaf if and…

In this paper we prove a new characterization of the distinguished unipotent orbits of a connected reductive group over an algebraically closed field of characteristic 0. For classical groups we prove the characterization by a combinatorial…

Let $G$ be a connected reductive group over $F_q$, where $q$ is large enough and the center of $G$ is connected. We are concerned with Lusztig's theory of {\em character sheaves}, a geometric version of the classical character theory of the…

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…

Let G_0 be a connected unipotent algebraic group over a finite field F_q, and let G be the unipotent group over an algebraic closure F of F_q obtained from G_0 by extension of scalars. If M is a Frobenius-invariant character sheaf on G, we…

Let G be a reductive connected group over an algebraic closure of a finite field. I define a tensor structure on the category of perverse sheaves on G which are direct sums of unipotent character sheaves in a fixed two-sided cell, in…

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…

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…

We introduce a class of perverse sheaves on a partial flag manifold of a connected reductive group G defined over a finite field which are equivariant under the action of the group of rational points of G. The definition of this class is…