Spherical representations of the Jacobi group
type: Item
instance of: scholarly article
title: Spherical representations of the Jacobi group
zbMATH Open document ID: 0958.11038
DOI: 10.1007/BF02942566
author: Ralf Schmidt
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2000-03-19T00:00:00Z
review text: Let \(G^J\) be the Jacobi group over a \(p\)-adic field. The author continues the earlier work (with \textit{R. Berndt}) [Elements of the representation theory of the Jacobi group. Progress in Mathematics 163, Birkhäuser, Basel (1998; Zbl 0931.11013)] and determines spherical vectors for admissible \(G^J\)-representations by explicit calculations in certain models. This leads to a complete classification of spherical representations in the ``almost good'' case: Besides the expected spherical principal series representations there are exactly three more. These can be explicitly associated to characters of the Hecke algebra. This result explains the local factors attached to a cuspidal Jacobi eigenform of squarefree index by \textit{J. Dulinski} [Result. Math. 31, 75-94 (1997; Zbl 0880.11044)].
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F50
zbMATH DE Number: 1416672
zbMATH Keywords: Jacobi group
zbMATH Keywords: spherical representation
zbMATH Keywords: Schrödinger-Weil representation
zbMATH Keywords: Hecke algebra
zbMATH Keywords: \(L\)-function
reviewed by: Aloys Krieg
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02942566
OpenAlex ID: W2006708614
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description: scientific article; zbMATH DE number 1416672