Restriction de la représentation de Weil à un sous-groupe compact maximal

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  • Maktouf Khemais
    Université de Monastir, Faculté des Sciences de Monastir, Département de Mathématiques
  • Torasso Pierre
    UMR 7348 CNRS, Université de Poitiers, Laboratoire de Mathématiques et Applications, Boulevard Marie et Pierre Curie

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  • Restriction de la representation de Weil a un sous-groupe compact maximal

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Abstract

Weil's representation is a basic object in representation theory which plays a crucial role in many places: construction of unitary irreducible representations in the frame of the orbit method, Howe correspondence, Theta series, … The decomposition in irreducibles of the restriction of Weil's representation to maximal compact subgroups or anisotropic tori of the metaplectic group is thus an important information in representation theory. Except for SL(2), this was not known in the p-adic case. In this article, we prove that the restriction of the Weil representation over a p-adic field, p ≠ 2, to maximal compact subgroups is multiplicity free and give an explicit description of the irreducibles occurring. In another paper, using our results, we describe the decomposition of the restriction of the Weil representation to maximal elliptic tori.

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