Related papers: On the Steinberg character of a reductive p-adic g…

We determine the irreducible constituents of the Steinberg character of an orthogonal group over a finite field restricted to the orthogonal group of one less dimension

This is a preliminary version of the first chapter of a book project on the character theory of finite groups of Lie type. It provides the foundations from the general theory of reductive algebraic groups over a finite field.

Let G be the p-adic group GL(n). Using C*-algebra techniques, we obtain a very explicit description of the tempered dual of G in terms of Bernstein parameters and extended quotients. We also prove that Plancherel measure (on the tempered…

We prove that the Jacquet restriction functor for a parabolic subgroup of a reductive group over a non-Archimedean local field is right adjoint to the parabolic induction functor for the opposite parabolic subgroup, in the generality of…

We use coefficient systems on the affine Bruhat-Tits building to study admissible representations of reductive p-adic groups in characteristic not equal to p. We show that the character function is locally constant and provide explicit…

This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturally the classification of irreducible square integrable representations modulo cuspidal data…

We compute the irreducible constitutents of the product of the Weil character and the Steinberg character in those finite classical groups for which a Weil character is defined, namely the symplectic, unitary and general linear groups. It…

Let G be a connected reductive group over an algebraic closure of a finite field Fq. In this paper it is proved that the infinite dimensional Steinberg module of kG defined by N. Xi in 2014 is irreducible when k is a field of positive…

Let $G$ be a simple algebraic group over an algebraically closed field of prime characteristic. If $M$ is a finite dimensional $G$-module that is projective over the Frobenius kernel of $G$, then its character is divisible by the character…

Let $G$ be a real or $p$-adic reductive group. We consider the tempered dual of $G$, and its connected components. For real groups, Wassermann proved in 1987, by noncommutative-geometric methods, that each connected component has a simple…

The character of an irreducible admissible representation of a $p$-adic reductive group is known to be a constant function in some neighborhood of any regular semisimple element $\gamma$ in the group. Under certain mild restrictions on…

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 state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.

In this note, we verify that several fundamental results from the theory of representations of reductive $p$-adic groups, extend to finite central extensions of these groups.

Let G be a semisimple, simply-connected algebraic group over an algebraically closed field of characteristic p > 0. We observe that the tensor product of the Steinberg module with a minuscule module is always indecomposable tilting.…

Let G be a semisimple almost simple algebraic group defined and split over a nonarchimedean local field K and let S be the Steinberg representation of G(K). Let t be be a very regular semisimple element of G(K). In this paper we give a…

We study the Picard groups of moduli spaces in positive characteristics and we give a "$p$-adic" proof that the Picard group of moduli of vector bundles of fixed determinant is isomorphic to the group of integers. Along the way we prove…

Let G be a reductive group over a non-archimedean local field and let S(G) be its Schwartz algebra. We compare Ext-groups of tempered G-representations in several module categories: smooth G-representations, algebraic S(G)-modules,…

This paper is an attempt to give some general results on the tempered fundamental group of a $p$-adic smooth algebraic varieties (which is a sort of analog of the topologic fundamental group of complex algebraic varieties in the p-adic…

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…