Related papers: Character Sheaves of Algebraic Groups Defined over…

Let F be a non-archimedean local field of odd residual characteristic p. Let G be a (connected) reductive group that splits over a tamely ramified field extension of F. We show that a construction analogous to Yu's construction of complex…

Given a smooth geometrically connected curve $C$ over a field $k$ and a smooth commutative group scheme $G$ of finite type over the function field $K$ of $C$ we study the Tate--Shafarevich groups given by elements of $H^1(K,G)$ locally…

I calculate characters of certain representations of loop groups based on non simply connected Lie groups. This gives a generalization of the Kac-Weyl character formula.

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 G be a connected unipotent group over a finite field F_q with q elements. In this article we propose a definition of L-packets of complex irreducible representations of the finite group G(F_q) and give an explicit description of…

For a reductive group G over a non-archimedean local field, we compare smooth representations over C with smooth representations over Qbar (an algebraic closure of Q). We show that an elliptic G-representation (in the sense of Arthur) can…

Let $G$ be a unipotent group over a field of characteristic $p > 0$. The theory of character sheaves on $G$ was initiated by V. Drinfeld and developed jointly with D. Boyarchenko. They also introduced the notion of $\mathbb{L}$-packets of…

Let G be a simple adjoint group and let K=k((\epsilon)) where k is an algebraic closure of a finite field F_q. In this paper we define some geometric objects on G(K) which are similar to the (cohomology sheaves of) the unipotent character…

Mirkovi\'c introduced the notion of character sheaves on a Lie algebra. Due to their simple geometric characterization, character sheaves on Lie algebras can be thought of as a simplified model for Lusztig's theory of character sheaves on…

Chevalley's theorem states that every smooth connected algebraic group over a perfect field is an extension of an abelian variety by a smooth connected affine group. That fails when the base field is not perfect. We define a pseudo-abelian…

This paper introduces the notion of locally algebraic representations and corresponding sheaves in the context of the cohomology of arithmetic groups. These representations are of relevance for the study of integral structures and special…

Let $N$ be a normal subgroup of a finite group $G$. From a result due to Brauer, it can be derived that the character table of $G$ contains square submatrices which are induced by the $G$-conjugacy classes of elements in $N$ and the…

Character tables of finite groups and closely related commutative algebras have been investigated recently using new perspectives arising from the AdS/CFT correspondence and low-dimensional topological quantum field theories. Two important…

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.

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…

Let k be a non-archimedean local field with residual characteristic p. Let G be a connected reductive group over k that splits over a tamely ramified field extension of k. Suppose p does not divide the order of the Weyl group of G. Then we…

We generalize results of P. Schneider and U. Stuhler for GL_l+1 to a reductive algebraic group G defined and split over a non-archimedean local field K. Following their lines, we prove that the generalized Steinberg representations of G…

We consider smooth representations of the unit group $G = \mathcal{A}^{\times}$ of a finite-dimensional split basic algebra $\mathcal{A}$ over a non-Archimedean local field. In particular, we prove a version of Gutkin's conjecture, namely,…

Among connected linear algebraic groups, quasi-reductive groups generalize pseudo-reductive groups, which in turn form a useful relaxation of the notion of reductivity. We study quasi-reductive groups over non-archimedean local fields,…

In this paper we investigate the representations of reductive groups over a finite field, introduced in 1987 by D.Kazhdan and G.Laumon. We show that generically these representations are irreducible and that their character is equal to the…