Endoscopy for unitary symmetric spaces

2019/10/21 by Spencer Leslie, Leslie, Spencer
Mathematics · #Advanced Algebra and Geometry #Advanced Harmonic Analysis Research #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1910.09685

openalex publication_date 2019/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by global applications, we propose a theory of relative endoscopic data and transfer factors for the symmetric pair (U(2n),U(n)× 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)× U(2)).

Citations

• Kudla--Rapoport cycles and derivatives of local densities
• The endoscopic fundamental lemma for unitary Friedberg-Jacquet periods

Related

• Exposing Relative Endoscopy in Unitary Symmetric Spaces
• Endoscopic transfer for unitary Lie algebras
• The endoscopic fundamental lemma for unitary Friedberg-Jacquet periods
• Endoscopy and cohomology of a quasi-split U(4)
• On the structure of endoscopic transfer factors