La conjecture locale de Gross-Prasad pour les représentations tempérées des groupes spéciaux orthogonaux

2009/11/24 by Jean-Loup Waldspurger, Waldspurger, Jean-Loup
Mathematics · #22E50 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:22E50

paper · pdf · doi:10.48550/arxiv.0911.4568

arxiv created 2009/11/24 · openalex publication_date 2009/11/24 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the local Gross-Prasad conjecture for tempered representations of special orthogonal groups. Roughly speaking, the conjecture says that, if sigma is an irreducible representation of SO(n) and rho is an irreducible representation of SO(n-1), rho appears as quotient of the restriction of sigma to SO(n-1) with a multiplicity m(sigma,rho) that can be computed in terms of epsilon-factors. Our proof uses results of a previous papers which computes m(sigma,rho) and the epsilon-factors by integral formulas.

Citations

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique

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