Haar measure on \(E_ q(2)\)
type: Item
instance of: scholarly article
title: Haar measure on \(E_ q(2)\)
zbMATH Open document ID: 0865.43001
published in: Pacific Journal of Mathematics
publication date: 1996-12-15T00:00:00Z
review text: Existence and uniqueness of an invariant weight on the quantum \(E(2)\) group is proved. The proof uses the knowledge of the Haar state on the quantum \(\text{SU} (2)\) group and exploits the fact that this group is related to \(E_q (2)\) through a contraction procedure. All irreducible unitary representations are found and orthogonality relations between their matrix entries are computed. It is found that unlike for a classical locally compact group with a two-sided invariant measure, any unitary representation can have square-integrable as well as non square-integrable matrix entries, which brings to fore the basis dependent nature of this quantum group. (E-mail: arup\@isid.ernet.in).
Mathematics Subject Classification ID: 43A05
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 950214
zbMATH Keywords: Haar measure
zbMATH Keywords: invariant weight
zbMATH Keywords: \(E_ q (2)\)
zbMATH Keywords: contraction
zbMATH Keywords: unitary representation
zbMATH Keywords: quantum group
author: Arup Kumar Pal
MaRDI profile type: Publication
full work available at URL: pjm.1996.176.217
OpenAlex ID: W2038948988
DOI: 10.2140/PJM.1996.176.217
description: scientific article; zbMATH DE number 950214