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Intégrales orbitales nilpotentes et endoscopie pour les groupes classiques non ramifiés / Jean-Loup Waldspurger

Auteur principal : Waldspurger, Jean-Loup, 1953-, AuteurType de document : MonographieCollection : Astérisque, 269Langue : français.Pays : France.Éditeur : Paris : Société mathématique de France, 2000Description : 1 vol. (449 p.) : fig. ; 24 cmISBN : 2856290965.ISSN : 0303-1179.Bibliographie : Bibliogr. p. [447]-449. Index.Sujet MSC : 22E35, Lie groups, Analysis on p-adic Lie groups
20G40, Linear algebraic groups and related topics, Linear algebraic groups over finite fields
20G25, Linear algebraic groups and related topics, Linear algebraic groups over local fields and their integers
11F70, Discontinuous groups and automorphic forms, Representation-theoretic methods; automorphic representations over local and global fields
11F72, Discontinuous groups and automorphic forms, Spectral theory; trace formulas
En-ligne : Résumé
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Séries SMF 269 (Browse shelf) Available 00549-01

This paper, a book in its own right, is devoted to clarifying two of the central questions which one encounters in trying to exploit the trace formula. Let G be an unramified classical group defined over a non-archimedean local field of characteristic 0 and residual characteristic p which is assumed to avoid an explicit finite set. Let g be its Lie algebra over F; the object which is investigated here is the set of stably invariant distributions on g which are supported on the set of nilpotent elements. This is achieved on p. 308. Let now H be an elliptic unramified endoscopic group of G. The second major result of the paper describes explicitly a transfer operator from the corresponding set of distributions for H to those for G. The analysis in this paper is primarily local in nature; it is very delicate and intricate with many subsidiary results, which the reviewer cannot hope to summarize here. (Zentralblatt)

Bibliogr. p. [447]-449. Index

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