On local Whittaker models for the Jacobi group of degree one
type: Item
instance of: scholarly article
title: On local Whittaker models for the Jacobi group of degree one
zbMATH Open document ID: 0827.11031
DOI: 10.1007/BF02567452
author: Rolf Berndt
published in: Manuscripta Mathematica
publication date: 1994-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155986
review text: The author studies the representation theory of the Jacobi group \(G^J\) of degree 1 over a local field \(F\), i.e. the semidirect product of the group \(\text{SL}_2 (F)\) with a Heisenberg group. In particular he addresses the question of existence and uniqueness of Whittaker models for unitary irreducible representations of this group. Existence and uniqueness are shown for the restriction of the functional to a certain subspace of the representation space (subject to some additional constraints on the representation studied). The main tool is the decomposition of the representation of \(G^J\) into the tensor product of the Weil representation of \(G^J\) and a representation of the metaplectic group. An alternative approach using differential equations is also discussed.
reviewed by: Rainer Schulze-Pillot
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F55
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 701161
zbMATH Keywords: Whittaker functional
zbMATH Keywords: Jacobi group
zbMATH Keywords: Whittaker models
zbMATH Keywords: irreducible representations
zbMATH Keywords: Weil representation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 701161