The endoscopic fundamental lemma for unitary Friedberg-Jacquet periods

Abstract

We prove the endoscopic fundamental lemma for the Lie algebra of the symmetric space $U(2n)/U(n)\times U(n)$, where $U(n)$ denotes a unitary group of rank $n$. This is the first major step in the stabilization of the relative trace formula associated to the $U(n)\times U(n)$-periods of automorphic forms on $U(2n)$.

arXiv comment89 pages. Accepted version, to appear in Annals of Mathematics

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• The fundamental lemma of Jacquet-Rallis in positive characteristics
• Kudla--Rapoport cycles and derivatives of local densities
• Multiplicity one Conjectures
• Weil representation and Arithmetic Fundamental Lemma
• Anticyclotomic Euler systems for unitary groups
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Cited by in corpus (4)

• Unitary Friedberg-Jacquet periods
• An analogue of the Grothendieck-Springer resolution for symmetric spaces
• Endoscopy for unitary symmetric spaces
• Endoscopic Relative Orbital Integrals on U${}_3$