Bessel functions on quaternionic Siegel domains
type: Item
instance of: scholarly article
title: Bessel functions on quaternionic Siegel domains
zbMATH Open document ID: 0814.43004
author: Hongming Ding
published in: Journal of Functional Analysis
publication date: 1995-06-12T00:00:00Z
review text: This article is part of a series of papers by the author on harmonic analysis on Hermitian symmetric spaces. The space under study here is \(G/K\), where \(G\) is the group \(O_ *(4n + 2)\) and \(K\) is a maximal compact subgroup, a Siegel domain of type II. The author considers the Segal-Shale-Weil (or harmonic) representation of \(G\) on a Schrödinger- Fock space (an \(L^ 2\) space of holomorphic functions). Making use of operator-valued Bessel and gamma functions, he obtains the main result of the paper: the Segal-Shale-Weil representation decomposes into a direct sum of irreducible components unitarily equivalent (by means of a Laplace transform) to holomorphic discrete series representations of \(G\).
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 599747
zbMATH Keywords: Hermitian symmetric spaces
zbMATH Keywords: Siegel domain
zbMATH Keywords: Schrödinger-Fock space
zbMATH Keywords: gamma functions
zbMATH Keywords: Segal-Shale-Weil representation
zbMATH Keywords: direct sum of irreducible components
zbMATH Keywords: Laplace transform
zbMATH Keywords: holomorphic discrete series representations
reviewed by: François Rouvière
MaRDI profile type: Publication
full work available at URL: jfan.1994.1021
OpenAlex ID: W1983328153
DOI: 10.1006/JFAN.1994.1021
description: scientific article; zbMATH DE number 599747