Journal of the Mathematical Society of Japan

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

Khemais MAKTOUF and Pierre TORASSO

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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.

Article information

Source
J. Math. Soc. Japan, Volume 68, Number 1 (2016), 245-293.

Dates
First available in Project Euclid: 25 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1453731542

Digital Object Identifier
doi:10.2969/jmsj/06810245

Mathematical Reviews number (MathSciNet)
MR3454560

Zentralblatt MATH identifier
1341.22015

Subjects
Primary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]

Keywords
Weil representation metaplectic group maximal compact subgroup elliptic maximal torus

Citation

MAKTOUF, Khemais; TORASSO, Pierre. Restriction de la représentation de Weil à un sous-groupe compact maximal. J. Math. Soc. Japan 68 (2016), no. 1, 245--293. doi:10.2969/jmsj/06810245. https://projecteuclid.org/euclid.jmsj/1453731542


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