Haar measure on E_q(2)

Arup Kumar Pal

Vol. 176 (1996), No. 1, 217–233

DOI: 10.2140/pjm.1996.176.217

Abstract

The quantum E(2) group is one of the simplest known examples so far of a locally compact noncompact quantum group. The existence and uniqueness of an ‘invariant measure’ on this group has been proved in this article. Using the invariant measure, we compute certain orthogonality relations, which then tells us that any unitary representation can have both square-integrable and non square-integrable matrix entries.

Mathematical Subject Classification 2000

Secondary: 81R50, 58B30, 46L89

Milestones

Received: 28 September 1994

Revised: 10 October 1995

Published: 1 November 1996