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Transfert d’intégrales orbitales pour le groupe métaplectique

Part of: Discontinuous groups and automorphic forms Lie groups

Published online by Cambridge University Press:  07 September 2010

Wen-Wei Li
Wen-Wei Li*
Affiliation:
Institut de Mathématiques de Jussieu – Université Paris Diderot 7, 175 rue du Chevaleret, 75013 Paris, France (email: wenweili@math.jussieu.fr)
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Abstract

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We set up a formalism of endoscopy for metaplectic groups. By defining a suitable transfer factor, we prove an analogue of the Langlands–Shelstad transfer conjecture for orbital integrals over any local field of characteristic zero, as well as the fundamental lemma for units of the Hecke algebra in the unramified case. This generalizes prior work of Adams and Renard in the real case and serves as a first step in studying the Arthur–Selberg trace formula for metaplectic groups.

Keywords

endoscopymetaplectic grouporbital integralLanglands–Shelstad conjecturefundamental lemma

MSC classification

Secondary: 22E35: Analysis on $p$-adic Lie groups 11F72: Spectral theory; Selberg trace formula 22E30: Analysis on real and complex Lie groups 22E50: Representations of Lie and linear algebraic groups over local fields
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 2 , March 2011 , pp. 524 - 590
Copyright
Copyright © Foundation Compositio Mathematica 2010

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