Open Access

Exposing relative endoscopy in unitary symmetric spaces

Research in the Mathematical Sciences20152:9

DOI: 10.1186/s40687-015-0024-y

Received: 22 December 2014

Accepted: 8 March 2015

Published: 10 July 2015

Abstract

We introduce a new class of symmetric space orbital integrals important for applications in certain relative trace formula appearing in the theory of automorphic representations. We verify a fundamental lemma for U2×U2U4 via an explicit calculation, giving the first known example of endoscopy for symmetric spaces and showing strong evidence that there is a general theory of endoscopy lurking in this situation.

AMS subject classification Primary 20G05

Keywords

Endoscopy Orbital integral Unitary group Trace formula Representation theory