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Pré-Publication, Document De Travail Année : 2022

The wave front set correspondence for dual pairs with one member compact

M Mckee
  • Fonction : Auteur
Angela Pasquale

Résumé

Let W be a real symplectic space and (G, G0) an irreducible dual pair in Sp(W), in the sense of Howe, with G compact. Let G be the preimage of G in the emetaplectic group Sp(W). Given an irreducible unitary representation Π of f G that occurs e in the restriction of the Weil representation to G, let Θ e Π denote its character. We prove that, for a suitable embedding T of Sp(W) in the space of tempered distributions on W, f the distribution T(Θˇ Π) admits an asymptotic limit, and the limit is a nilpotent orbital integral. As an application, we compute the wave front set of Π0, the representation of Gf0 dual to Π, by elementary means
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Dates et versions

hal-03324770 , version 1 (23-08-2021)
hal-03324770 , version 2 (27-12-2022)

Identifiants

  • HAL Id : hal-03324770 , version 2

Citer

M Mckee, Angela Pasquale, T Przebinda. The wave front set correspondence for dual pairs with one member compact. 2022. ⟨hal-03324770v2⟩
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