A contraction of SU(2) to the Heisenberg group
type: Item
instance of: scholarly article
title: A contraction of SU(2) to the Heisenberg group
zbMATH Open document ID: 0588.43007
DOI: 10.1007/BF01301660
author: Fulvio Ricci
published in: Monatshefte für Mathematik
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178275
review text: If a ball in two complex dimensions is subject to an appropriate one- parameter family of non-isotropic dilations, it tends to cover in the limit the Siegel domain defined by Im \(z_ 2> | z_ 1|^ 2\). If the boundary of the ball is identified with the special unitary group SU(2) and the boundary of the Siegel domain with the three-dimensional Heisenberg group H, this procedure induces a contraction of SU(2) to H. It is shown how this picture allows to realize the infinite-dimensional representations of H as limits of irreducibles of SU(2).
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 22E27
Mathematics Subject Classification ID: 32M99
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 32A07
zbMATH DE Number: 3944509
zbMATH Keywords: Lie group contractions
zbMATH Keywords: ball
zbMATH Keywords: one-parameter family
zbMATH Keywords: non-isotropic dilations
zbMATH Keywords: Siegel domain
zbMATH Keywords: special unitary group
zbMATH Keywords: Heisenberg group
zbMATH Keywords: infinite-dimensional representations
zbMATH Keywords: limits of irreducibles
MaRDI profile type: Publication
Wikidata QID: Q126096384
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description: scientific article; zbMATH DE number 3944509