A note on Standard Modules and Vogan L-packets
| Autor: | Volker Heiermann |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), ANR-13-BS01-0012,FERPLAY,Formule des Traces Relative, Périodes, Fonctions L et Analyse Harmonique(2013) |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Mathematics - Number Theory
Group (mathematics) Mathematics::Number Theory General Mathematics 010102 general mathematics Algebraic geometry Reductive group 01 natural sciences Prime (order theory) [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] Jacquet module Combinatorics Number theory 0103 physical sciences FOS: Mathematics Tempered representation Number Theory (math.NT) 010307 mathematical physics Representation Theory (math.RT) 0101 mathematics Mathematics::Representation Theory Mathematics - Representation Theory Quotient ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | manuscripta mathematica manuscripta mathematica, Springer Verlag, 2016, 150, pp.571-583. ⟨10.1007/s00229-016-0824-4⟩ Manuscripta mathematica Manuscripta mathematica, 2016, 150, pp.571-583. ⟨10.1007/s00229-016-0824-4⟩ |
| ISSN: | 0025-2611 1432-1785 |
| DOI: | 10.1007/s00229-016-0824-4⟩ |
| Popis: | Let $F$ be a non-Archimedean local field of characteristic $0$, let $G$ be the group of $F$-rational points of a connected reductive group defined over $F$ and let $G'$ be the group of $F$-rational points of its quasi-split inner form. Given standard modules $I(\tau ,\nu )$ and $I(\tau ',\nu ')$ for $G$ and $G'$ respectively with $\tau '$ a generic tempered representation, such that the Harish-Chandra's $\mu $-functions of a representation in the supercuspidal support of $\tau $ and of a generic essentially square-integral representation in some Jacquet module of $\tau '$ agree (after a suitable identification of the underlying spaces under which $\nu =\nu '$), we show that $I(\tau ,\nu )$ is irreducible whenever $I(\tau ',\nu ')$ is. The conditions are satisfied if the Langlands quotients $J(\tau ,\nu )$ and $J(\tau ',\nu ')$ of respectively $I(\tau ,\nu )$ and $I(\tau ',\nu ')$ lie in the same Vogan $L$-packet (whenever this Vogan $L$-packet is defined), proving that, for any Vogan $L$-packet, all the standard modules whose Langlands quotient is equal to a member of the Vogan $L$-packet are irreducible, if and only if this Vogan $L$-packet contains a generic representation. The result for generic Vogan $L$-packets of quasi-split orthogonal and symplectic groups was proven by Moeglin-Waldspurger and used in their proof of the general case of the local Gan-Gross-Prasad conjectures for these Groups. Comment: 15 pages |
| Databáze: | OpenAIRE |
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