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January, 2016 Restriction de la représentation de Weil à un sous-groupe compact maximal
Khemais MAKTOUF, Pierre TORASSO
J. Math. Soc. Japan 68(1): 245-293 (January, 2016). DOI: 10.2969/jmsj/06810245

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, $p\neq2$, 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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Khemais MAKTOUF. Pierre TORASSO. "Restriction de la représentation de Weil à un sous-groupe compact maximal." J. Math. Soc. Japan 68 (1) 245 - 293, January, 2016. https://doi.org/10.2969/jmsj/06810245

Information

Published: January, 2016
First available in Project Euclid: 25 January 2016

zbMATH: 1341.22015
MathSciNet: MR3454560
Digital Object Identifier: 10.2969/jmsj/06810245

Subjects:
Primary: 22E50

Rights: Copyright © 2016 Mathematical Society of Japan

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Vol.68 • No. 1 • January, 2016
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