Given a p-adic group G=G(F) and finite Γ⊂AutF(G) such that the fixed-point subgroup GΓ is reductive, we establish relationship between constructions of types for G due to Yu, Kim–Yu Fintzen, which generalizes those general linear classical groups originally observed by Stevens. As an application, given irreducible representation π G, explicitly identify number inertial equivalence classes occur...

Consider the character of an irreducible admissible representation of a p-adic reductive group. The Harish-Chandra-Howe local expansion expresses this character near a semisimple element as a linear combination of Fourier transforms of nilpotent orbital integrals. Under mild hypotheses, we describe an explicit region on which the local character expansion is valid. We assume neither that the gr...

Abstract Let k be an algebraically closed field of characteristic p > 2. We compute the Weyl filtration multiplicities in indecomposable tilting modules and decomposition numbers for symplectic group over terms cap-curl diagrams under assumption that is bigger than greatest hook length largest partition involved. As a corollary we obtain Brauer algebra same assumptions. Our work combines ide...

New results in the representation theory of “semisimple” algebraic monoids are obtained, based on Renner’s monoid version of Chevalley’s big cell. (The semisimple algebraic monoids have been classified by Renner.) The rational representations of such a monoid are the same thing as “polynomial” representations of the associated reductive group of units in the monoid, and this representation cate...

In this paper we construct certain moduli spaces, which we call moduli spaces of (principal) F -bundles, and study their basic properties. These spaces are associated to triples consisting of a smooth projective geometrically connected curve over a finite field, a split reductive group G, and an irreducible algebraic representation ω of (Ǧ)n/Z(Ǧ). Our spaces generalize moduli spaces of F -sheav...

Let G be a connected linear semisimple Lie group having a Holomorphic Discrete Series representation π. Let H be a connected reductive subgroupof G so that the global symmetric space attached to H is a real form of the Hermitian symmetric space associated to G. Fix a maximal compact subgroup K of G so that H ∩ K is a maximal compact subgroup for H. Let τ be the lowest K−type for π and let τ? de...

Write Θ for the stable character associated to a finite dimensional representation E of a connected real reductive group G. Let M be the centralizer of a maximal torus T , and denote by ΦM (γ,Θ ) Arthur’s extension of |D M (γ)| 1 2Θ(γ) to T (R). In this paper we give a simple explicit expression for ΦM (γ,Θ ), when γ is elliptic in G.

For a fairly general reductive group G/Qp , we explicitly compute the space of locally algebraic vectors in the Breuil-Herzig construction Π(ρ)ord, for a potentially semistable Borel-valued representation ρ of Gal(Q̄p/Qp). The point being we deal with the whole representation, not just its socle – and we go beyond GLn(Qp). In the case of GL2(Qp), this relation is one of the key properties of the...

In this paper, we give a concrete description of the two-fold cover of a simply connected, split real reductive group and its maximal compact subgroup as Chevalley groups. We study the representations of the maximal compact subgroups called pseudospherical representations which appear with multiplicity one in the principal series representation. We introduce a family of canonically defined inte...

we present the basic results on the representation theory of the alternating groups. our approach is based on clifford theory.