Restriction de la repr 'esentation de Weil `a un sous-groupe compact\n maximal ou `a un tore maximal elliptique

2011/01/03 by Khemais Maktouf, Maktouf, Khemais, Pierre Torasso +1 · 1 citation
Mathematics · #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1101.0560

openalex publication_date 2011/01/03 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Weil's representation is a basic object in representation theory which plays\na crucial role in many places: construction of unitary irreducible\nrepresentations in the frame of the orbit method, Howe correspondence, Theta\nseries,... The decomposition in irreducible of the restriction of Weil's\nrepresentation to maximal compact subgroups or anisotropic tori of the\nmetaplectic group is thus an important information in representation theory.\nExcept for SL(2), this was not known in the p-adic case. In this article, we\nprove that the restriction of the Weil representation over a p-adic field, p\ndifferent from 2, to maximal compact subgroups or maximal elliptic tori is\nmultiplicity free and give an explicit description of the irreducible\nrepresentations or characters occurring.\n

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