On the transfer of distributions: Weighted orbital integrals

On the Transfer of Distributions: Weighted Orbital Integrals

0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 1. Multiple groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 2. K-groups and transfer factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 3. ...

Weighted orbital integrals

This is an expanded version of a survey talk given at the Conference on Representations of Real Reductive Lie Groups, June 4 to June 8, 2006, at the Snowbird Mountain Resort, Utah. We explain the definition of weighted orbital integrals and their Fourier transforms and report their known properties, leaving aside questions of endoscopy. We also announce some new results on those Fourier transfo...

The Local Behaviour of Weighted Orbital Integrals

are obtained by integrating f with respect to the invariant measure on the conjugacy class of y. They are of considerable importance for the harmonic analysis of G(F). Invariant orbital integrals are also of interest because they occur on the geometric side of the trace formula, in the case of compact quotient. For the general trace formula, the analogous terms are weighted orbital integrals [3...

On the Fourier transforms of weighted orbital integrals

The characters of supercuspidal representations as weighted orbital integrals

Weighted orbital integrals are the terms which occur on the geometric side of the trace formula. We shall investigate these distributions on a p-adic group. We shall evaluate the weighted orbital integral of a supercuspidal matrix coefficient as a multiple of the corresponding character.