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

Maktouf, Khemais; Torasso, Pierre

doi:10.2969/jmsj/06810245

Cited by 3 publications

(3 citation statements)

References 19 publications

(23 reference statements)

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“…-Any F -distinguished orbit is quasi-admissible, since for such orbits M γ is trivial. Over non-Archimedean F , F -distinguished orbits are admissible since the metaplectic cover splits over compact subgroups, see [38,Theorem 4.6.1]. Over F = R, the minimal orbit in U (2, 1) is Rdistinguished but not admissible.…”

Section: Proof Of Theorem 13mentioning

confidence: 99%

Whittaker supports for representations of reductive groups

Gomez¹,

Gourevitch²,

Sahi³

2021

Annales De l'Institut Fourier

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Section: Proof Of Theorem 13mentioning

confidence: 99%

Whittaker supports for representations of reductive groups

Gomez¹,

Gourevitch²,

Sahi³

2021

Annales De l'Institut Fourier

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“…Any F -distinguished orbit is quasi-admissible, since for such orbits M γ is trivial. Over non-Archimedean F , F -distinguished orbits are admissible since the metaplectic cover splits over compact subgroups, see [MT16]. Over F = R, the minimal orbit in U (2, 1) is Rdistinguished but not admissible.…”

Section: Proof Of Theorem Bmentioning

confidence: 99%

Whittaker supports for representations of reductive groups

Moreno¹,

Gourevitch²,

Sahi³

2016

Preprint

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Let F be either R or a finite extension of Qp, and let G be a finite central extension of the group of F -points of a reductive group defined over F . Also let π be a smooth representation of G (Fréchet of moderate growth if F = R). For each nilpotent orbit O we consider a certain Whittaker quotient πO of π. We define the Whittaker support WS(π) to be the set of maximal O among those for which πO = 0.In this paper we prove that all O ∈ WS(π) are quasi-admissible nilpotent orbits, generalizing some of the results in [Moe96, JLS16]. If F is p-adic and π is quasi-cuspidal then we show that all O ∈ WS(π) are F -distinguished, i.e. do not intersect the Lie algebra of any proper Levi subgroup of G defined over F .We also give an adaptation of our argument to automorphic representations, generalizing some results from [GRS03, Shen16, JLS16, Cai] and confirming a conjecture from [Gin06].Our methods are a synergy of the methods of the above-mentioned papers, and of our preceding paper [GGS17].

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“…A small part of the decomposition has been explained in the general case (Cliff-McNeilly-Szechtman [4]). In their paper [14], Maktouf and Torasso have shown that the restriction of the Weil representation of a symplectic group over a p-adic field to a maximal compact subgroup or to a maximal elliptic torus is multiplicity-free and have given an explicit description of the irreducible subrepresentations.…”

mentioning

confidence: 99%

Combinatorics of finite abelian groups and Weil representations

Dutta

Prasad

2015

Pacific J. Math.

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The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil representation are parametrized by a partially ordered set which is independent of p. As p varies, the dimension of the irreducible representation corresponding to each parameter is shown to be a polynomial in p which is calculated explicitly. The commuting algebra of the Weil representation has a basis indexed by another partially ordered set which is independent of p. The expansions of the projection operators onto the irreducible invariant subspaces in terms of this basis are calculated. The coefficients are again polynomials in p. These results remain valid in the more general setting of finitely generated torsion modules over a Dedekind domain.Comment: 26 pages, 3 figures Revised version, to appear in Pacific Journal of Mathematic

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

Cited by 3 publications

References 19 publications

Whittaker supports for representations of reductive groups

Whittaker supports for representations of reductive groups

Whittaker supports for representations of reductive groups

Combinatorics of finite abelian groups and Weil representations

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