%0 Journal Article
%T Expression d'un facteur epsilon de paire par une formule intégrale
%+ Institut de Mathématiques de Jussieu (IMJ)
%A Beuzart-Plessis, Raphaël
%Z 58p.
%< avec comité de lecture
%@ 0008-414X
%J Canadian Journal of Mathematics
%I University of Toronto Press
%V 66
%N 5
%P 993-1049
%8 2014-10-01
%D 2014
%Z 1212.1082
%R 10.4153/CJM-2013-042-4
%K twisted groups
%K epsilon factor
%Z Mathematics [math]/Representation Theory [math.RT]
%Z Mathematics [math]/Number Theory [math.NT]Journal articles
%X Let $E/F$ be a quadratic extension of $p$-adic fields and let $d$, $m$ be nonnegative integers of distinct parities. Fix admissible irreducible tempered representations $\pi$ and $\sigma$ of $GL_d(E)$ and $GL_m(E)$ respectively. We assume that $\pi$ and $\sigma$ are conjugate-dual. That is to say $\pi\simeq \pi^{\vee,c}$ and $\sigma\simeq \sigma^{\vee,c}$) where $c$ is the non trivial $F$-automorphism of $E$. This implies, we can extend $\pi$ to an unitary representation $\tilde{\pi}$ of a nonconnected group $GL_d(E)\rtimes \{1,\theta\}$. Define $\tilde{\sigma}$ the same way. We state and prove an integral formula for $\epsilon(1/2,\pi\times \sigma,\psi_E)$ involving the characters of $\tilde{\pi}$ and $\tilde{\sigma}$. This formula is related to the local Gan-Gross-Prasad conjecture for unitary groups.
%G French
%2 https://hal.science/hal-00761080v2/document
%2 https://hal.science/hal-00761080v2/file/articleeps-1.pdf
%L hal-00761080
%U https://hal.science/hal-00761080
%~ UNIV-PARIS7
%~ UPMC
%~ CNRS
%~ IMJ
%~ UPMC_POLE_1
%~ SORBONNE-UNIVERSITE
%~ SU-SCIENCES
%~ UNIV-PARIS
%~ UP-SCIENCES
%~ SU-TI
%~ ALLIANCE-SU