Endoscopy for unitary symmetric spaces

Spencer Leslie

Published 2019-10-21Version 1

Motivated by global applications, we propose a theory of relative endoscopic data and transfer factors for the symmetric pair $(U(2n),U(n)\times U(n))$ over a local field. We then formulate the smooth transfer and fundamental lemma conjectures, establish the existence of smooth transfer for many test functions, and prove the fundamental lemma for the symmetric pair $(U(4),U(2)\times U(2))$.