An Example of Fourier Transforms of Orbital Integrals and their Endoscopic Transfer

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...

On the Fourier transforms of weighted orbital integrals

Endoscopic Transfer of Orbital Integrals in Large Residual Characteristic Julia Gordon and Thomas Hales

This article constructs Shalika germs in the context of motivic integration, both for ordinary orbital integrals and κ-orbital integrals. Based on transfer principles in motivic integration and on Waldspurger’s endoscopic transfer of smooth functions in characteristic zero, we deduce the endoscopic transfer of smooth functions in sufficiently large residual characteristic. We dedicate this arti...

BOUNDS FOR FOURIER TRANSFORMS OF REGULAR ORBITAL INTEGRALS ON p-ADIC LIE ALGEBRAS

Let G be a connected reductive p-adic group and let g be its Lie algebra. LetO be a G-orbit in g. Then the orbital integral μO corresponding to O is an invariant distribution on g, and Harish-Chandra proved that its Fourier transform μ̂O is a locally constant function on the set g′ of regular semisimple elements of g. Furthermore, he showed that a normalized version of the Fourier transform is l...

On the Transfer of Distributions: Weighted Orbital Integrals

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