Howe duality and the trace formula

Zhengyu Mao and Stephen Rallis

Vol. 191 (1999), No. 2, 329–346

DOI: 10.2140/pjm.1999.191.329

Abstract

We state two families of trace formulas for the Howe duality. We prove the matching of orbital integrals for the trace formulas. The fundamental lemma (matching of orbital integrals for spherical functions) turns out to be the consequence of local Howe duality. We use the local Howe duality to prove the fundamental lemmas for another interesting family of trace formulas.

Milestones

Received: 2 February 1998

Revised: 10 February 1999

Published: 1 December 1999