Endoscopy for unitary symmetric spaces

Abstract

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 conjecture and fundamental lemma, establish the existence of smooth transfer for many test functions, and prove the fundamental lemma for the symmetric pair $(U(4),U(2)\times U(2))$.

arXiv commentEdits throughout; several small errors corrected and improved exposition on transfer factors

References in corpus (6)

• The dual group of a spherical variety
• Kudla--Rapoport cycles and derivatives of local densities
• On the smooth transfer for Guo-Jacquet relative trace formulae
• The endoscopic fundamental lemma for unitary Friedberg-Jacquet periods
• Hodge classes and the Jacquet-Langlands correspondence
• Endoscopic transfer for unitary Lie algebras

Cited by in corpus (2)

• The endoscopic fundamental lemma for unitary Friedberg-Jacquet periods
• Unitary Friedberg-Jacquet periods