Laurent Clozel

Orbital Integrals on p-adic Groups: A Proof of the Howe Conjecture

Let G be a connected reductive group over a p-adic field F of characteristic 0. Let G = G(F). Let o be a compact subset of G, oG the invariant subset { gxg1: g E G, x E co} of G. We say that a closed invariant subset of G, Q, is compact modulo conjugation if Q c wG for some compact co. (It is equivalent to assume that the traces of Q on all Cartan subgroups of G are compact.) The purpose of this article is to prove the following theorem concerning invariant distributions on G, which had been conjectured by Howe [10]. Let Of(Q) denote the set of invariant distributions supported in U. If K is a compact-open subgroup of G, let XK be the Hecke algebra of compactly supported functions on G with complex values, invariant on the left and right by K.

Invariant Harmonic Analysis on the Schwartz Space of a Reductive p-ADIC Group

At the Williastown conference on harmonic analysis, R. Howe publicized two conjectures concerning the orbital integrals of functions on a reductive p-adic group and on its Lie algebra. He proved the Lie algebra case of the conjecture himself; recently we have proved the conjecture on the group, at least in zero characteristic [4c,4d].

equidistribution de mesures algébriques

2 Tores, groupes resolubles, cas R-anisotrope. 11 2.1 Le cas des tores anisotropes . . . . . . . . . . . . . . . . . . . 11 2.1.1 La propriete (E) pour les tores anisotropes . . . . . . . 12 2.1.2 La propriete (Ea) pour les tores anisotropes . . . . . . . 13 2.2 Groupes resolubles . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 Groupes semi-simples R-anisotropes . . . . . . . . . . . . . . . 19

Level-raising and symmetric power functoriality, III

We apply automorphy lifting techniques to establish new cases of symmetric power functoriality for Hilbert modular forms of regular algebraic weight. The proof is based on a novel application of an automorphy lifting theorem for residually reducible Galois representations.

Level-raising and symmetric power functoriality, I

As the simplest case of Langlands functoriality, one expects the existence of the symmetric power

Hecke operators and equidistribution of Hecke points

S^n(\pi )

On the cohomology of Kottwitz’s arithmetic varieties

, where

The fundamental lemma for stable base change

\pi

Correspondances modulaires et mesures invariantes

is an automorphic representation of

EQUIDISTRIBUTION DES POINTS DE HECKE

{\rm GL}(2,{\mathbb{A}})