Invariant Functionals on Speh Representations

Gourevitch, Dmitry; Sahi, Siddhartha; Sayag, Eitan

doi:10.1007/s00031-015-9345-6

Cited by 7 publications

(7 citation statements)

References 37 publications

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“…We conjecture that µ ω is the unique Sp(V )-invariant distribution on Gr 2k (V ). This was shown by Gourevitch, Sahi and Sayag in [GSS15] for k = n when n is even.…”

Section: Proof Let [[B]] Be the Current Defined By B Then [B]supporting

confidence: 58%

Contact integral geometry and the Heisenberg algebra

Faifman

2019

Geom. Topol.

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Generalizing Weyl's tube formula and building on Chern's work, Alesker reinterpreted the Lipschitz-Killing curvature integrals as a family of valuations (finitely-additive measures with good analytic properties), attached canonically to any Riemannian manifold, which is universal with respect to isometric embeddings. In this note, we uncover a similar structure for contact manifolds. Namely, we show that a contact manifold admits a canonical family of generalized valuations, which are universal under contact embeddings. Those valuations assign numerical invariants to even-dimensional submanifolds, which in a certain sense measure the curvature at points of tangency to the contact structure. Moreover, these valuations generalize to the class of manifolds equipped with the structure of a Heisenberg algebra on their cotangent bundle. Pursuing the analogy with Euclidean integral geometry, we construct symplectic-invariant distributions on Grassmannians to produce Crofton formulas on the contact sphere. Using closely related distributions, we obtain Crofton formulas also in the linear symplectic space.

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“…We conjecture that µ ω is the unique Sp(V )-invariant distribution on Gr 2k (V ). This was shown by Gourevitch, Sahi and Sayag in [GSS15] for k = n when n is even.…”

Section: Proof Let [[B]] Be the Current Defined By B Then [B]supporting

confidence: 58%

Contact integral geometry and the Heisenberg algebra

Faifman

2019

Geom. Topol.

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“…[GK75, Sha74, JR96, Pra90, vD08, AGRS10, AGS08, HM08, AG09a, AG09b, SZ12, GGP12, OS08b]) and to the construction of bases to these spaces (e.g. [vB88,OS08a,GSS15]).…”

Section: Introductionmentioning

confidence: 99%

Homological multiplicities in representation theory of p-adic groups

Aizenbud

Sayag

2019

Math. Z.

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We study homological multiplicities of spherical varieties of reductive group G over a p-adic field F . Based on Bernstein's decomposition of the category of smooth representations of a p-adic group, we introduce a sheaf that measures these multiplicities.We show that these multiplicities are finite whenever the usual mutliplicities are finite, in particular this holds for symmetric varieties, conjectured for all spherical varieties and known for a large class of spherical varieties. Furthermore, we show that the Euler-Poincaré characteristic is constant in families induced from admissible representations of a Levi M. In the case when M = G we compute these multiplicities more explicitly.

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“…Recently, in [GSS15] a local construction of these invariant functionals is provided, based on tools from the theory of distributions and D-modules. Some of the results of the present work can be considered as a non-archimedean analogue of the main result of [GSS15]. 1.4.…”

Section: Proofs and Methodsmentioning

confidence: 99%

Klyachko models for ladder representations

Mitra¹,

Offen²,

Sayag³

2016

Preprint

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We give a new proof for the existence of Klyachko models for unitary representations of GL n (F ) over a non-archimedean local field F . Our methods are purely local and are based on studying distinction within the class of ladder representations introduced by Lapid and Mínguez. We classify those ladder representations that are distinguished with respect to Klyachko models. We prove the hereditary property of these models for induced representations from arbitrary finite length representations. Finally, in the other direction and in the context of admissible representations induced from ladder, we study the relation between distinction of the parabolic induction with respect to the symplectic groups and distinction of the inducing data.

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Invariant Functionals on Speh Representations

Cited by 7 publications

References 37 publications

Contact integral geometry and the Heisenberg algebra

Contact integral geometry and the Heisenberg algebra

Homological multiplicities in representation theory of p-adic groups

Klyachko models for ladder representations

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