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Jean-Loup Waldspurger

  1. La conjecture locale de Gross-Prasad pour les groupes sp\'eciaux orthogonaux: le cas g\'en\'eral.

    Thu, 01/07/2010 - 16:01 — SomNambul
    Authors: Jean-Loup Waldspurger, Colette Moeglin
    Subjects: Representation Theory
    Abstract

    We prove the local Gross-Prasad conjecture for generic L-packets of
    representations of special orthogonal groups. The proof uses the same result
    for tempered L-packets proved in a preceding paper, and irreducibility results
    for the induced representations of whose the elements of the L-packets are
    Langlands quotients.

  2. La conjecture locale de Gross-Prasad pour les repr\'esentations temp\'er\'ees des groupes sp\'eciaux orthogonaux.

    Wed, 11/25/2009 - 16:01 — SomNambul
    Authors: Jean-Loup Waldspurger
    Subjects: Representation Theory
    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.

  3. Calcul d'une valeur d'un facteur epsilon par une formule int\'egrale.

    Wed, 10/14/2009 - 11:03 — SomNambul
    Authors: Jean-Loup Waldspurger
    Subjects: Representation Theory
    Abstract

    Let d and m be two natural numbers of distinct parities. Let $\pi$ be an
    admissible irreducible tempered representation of GL(d,F), where F is a p-adic
    field. We assume that $\pi$ is self-dual. Then we can extend $\pi$ as a
    representation $\tilde{\pi}$ of a non-connected group $GL(d,F)\rtimes
    \{1,\theta\}$. Let $\rho$ be a representation of GL(m,F). We assume that it has
    similar properties as $\pi$. Jacquet, Piatetski-Shapiro and Shalika have
    defined the factor $\epsilon(s,\pi\times\rho,\psi)$.

  4. Calcul d'une valeur d'un facteur epsilon par une formule int\'egrale.

    Wed, 10/14/2009 - 11:03 — SomNambul
    Authors: Jean-Loup Waldspurger
    Subjects: Representation Theory
    Abstract

    Let d and m be two natural numbers of distinct parities. Let $\pi$ be an
    admissible irreducible tempered representation of GL(d,F), where F is a p-adic
    field. We assume that $\pi$ is self-dual. Then we can extend $\pi$ as a
    representation $\tilde{\pi}$ of a non-connected group $GL(d,F)\rtimes
    \{1,\theta\}$. Let $\rho$ be a representation of GL(m,F). We assume that it has
    similar properties as $\pi$. Jacquet, Piatetski-Shapiro and Shalika have
    defined the factor $\epsilon(s,\pi\times\rho,\psi)$.

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