La conjecture locale de Gross-Prasad pour les repr\'esentations temp\'er\'ees des groupes unitaires

By R. Beuzart-Plessis. 2012

71 citations recorded by the source corpus.

Let $E/F$ be a quadratic extension of non-archimedean local fields of characteristic 0 and let $G=U(n)$, $H=U(m)$ be unitary groups of hermitian spaces $V$ and $W$. Assume that $V$ contains $W$ and that the orthogonal complement of $W$ is a quasisplit hermitian space (i.e. whose unitary group is quasisplit over $F$). Let $\pi$ and $\sigma$ be smooth irreducible representations of $G(F)$ and $H(F)$ respectively. Then Gan, Gross and Prasad have defined a multiplicity $m(\pi,\sigma)$ which for $m=n-1$ is just the dimension of $Hom_{H(F)}(\pi,\sigma)$. For $\pi$ and $\sigma$ tempered, we state and prove an integral formula for this multiplicity. As a consequence, assuming some expected properties of tempered $L$-packets, we prove a part of the local Gross-Prasad conjecture for tempered representations of unitary groups. This article represents a straight continuation of recent papers of Waldspurger dealing with special orthogonal groups.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/65efb3c34d14dbe5684e92334cb20e4f10da4979

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In Discrete Mathematics and Combinatorics

  1. Michael Harris
  2. H. Grobner

In Geometry and Topology

  1. H. Grobner
  2. Michael Harris
  3. T. Gee
  4. Peter Scholze
  5. David Geraghty
  6. Ana Caraiani
  7. Thomas Barnet-Lamb
  8. W. Gan

In Mathematical Physics

  1. H. Grobner
  2. Michael Harris
  3. T. Gee
  4. Peter Scholze
  5. David Geraghty
  6. Ana Caraiani
  7. Thomas Barnet-Lamb
  8. W. Gan

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