Uniqueness and disjointness of Klyachko models

Offen, Omer; Sayag, Eitan

doi:10.1016/j.jfa.2008.01.004

Cited by 30 publications

(23 citation statements)

References 9 publications

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“…In particular, Kl 0 is the group of upper unitriangular matrices and Kl n = Sp n (F ) (if n is even). It is shown in [Kly84], [IS91], [HZ00] for finite fields F and in [HR90], [OS07], [OS08a], [OS08b], [OS09], [GOSS12], [AOS12] for local fields F that for any irreducible unitary representation π of GL n (F ) there exists a non-zero (Kl k , ψ k )-equivariant functional on π ∞ for exactly one k. The uniqueness of such functional is known only over non-archimedean fields (see [OS08b]). …”

Section: Related Resultsmentioning

confidence: 99%

Invariant Functionals on Speh Representations

Gourevitch

Sahi

Sayag

2015

Transformation Groups

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We study Sp 2n (R)-invariant functionals on the spaces of smooth vectors in Speh representations of GL 2n (R).For even n we give expressions for such invariant functionals using an explicit realization of the space of smooth vectors in the Speh representations. Furthermore, we show that the functional we construct is, up to a constant, the unique functional on the Speh representation which is invariant under the Siegel parabolic subgroup of Sp 2n (R). For odd n we show that the Speh representations do not admit an invariant functional with respect to the subgroup Un of Sp 2n (R) consisting of unitary matrices.Our construction, combined with the argument in [GOSS12], gives a purely local and explicit construction of Klyachko models for all unitary representations of GLn(R).

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Section: Related Resultsmentioning

confidence: 99%

Invariant Functionals on Speh Representations

Gourevitch

Sahi

Sayag

2015

Transformation Groups

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“…The important properties and applications of the Klyachko models are referred to a recent work of Offen and Sayag [39][40][41]. It seems reasonable to expect that the new family of the ψ Sr,n -models for GL 2n has the similar possible applications to representation theory and automorphic forms.…”

Section: Further Properties Of the Generalized Shalika Modelsmentioning

confidence: 99%

Symplectic supercuspidal representations and related problems

2010

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“…Then invoking Theorem 1.4 enables us to further reduce the problem, to the vanishing of (ind Q n St ψ k U n (ω ψ ⊗ ω ψ −1 )) N n ,ψ , which essentially follows from the results of Offen and Sayag on Klyachko models ( [55], see also [43]). …”

Section: Distinguished Representationsmentioning

confidence: 95%

Theta distinguished representations, inflation and the symmetric square L-function

Kaplan

2016

Math. Z.

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A theta distinguished representation is a quotient of a tensor of exceptional representations, where "exceptional" is in the sense of Kazhdan and Patterson. We study relations between theta distinguished representations of GL n and GSpin 2n+1 . In the case of GSpin 2n+1 (or SO 2n+1 ) exceptional (or small) representations were constructed by Bump, Friedberg and Ginzburg. We prove a Rodier-type hereditary property: a tempered representation τ is distinguished if and only if the representation I(τ ) induced to GSpin 2n+1 is distinguished, and the multiplicity of both quotients is at most one. If τ is supercuspidal and distinguished, then so is the Langlands quotient of I(τ ). As a corollary, we characterize supercuspidal distinguished representations, in terms of the pole of the symmetric square L-function at s = 0.

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Uniqueness and disjointness of Klyachko models

Abstract: We show the uniqueness and disjointness of Klyachko models for GL n over a non-Archimedean local field. This completes, in particular, the study of Klyachko models on the unitary dual. Our local results imply a global rigidity property for the discrete automorphic spectrum of GL n .

Cited by 30 publications

References 9 publications

Invariant Functionals on Speh Representations

Invariant Functionals on Speh Representations

Symplectic supercuspidal representations and related problems

Theta distinguished representations, inflation and the symmetric square L-function

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