Journal of Lie Theory 21 (2011), No. 4, 905--928
Copyright Heldermann Verlag 2011
Modular Properties of Matrix Coefficients of Corepresentations of a Locally Compact Quantum Group
Martijn Caspers
Radboud Universiteit, IMAPP, Heyendaalseweg 135, Nijmegen, 6525 AJ, The Netherlands
caspers@math.ru.nl
Erik Koelink
Radboud Universiteit, IMAPP, Heyendaalseweg 135, Nijmegen, 6525 AJ, The Netherlands
e.koelink@math.ru.nl
We give a formula for the modular operator and modular conjugation in terms of matrix coefficients of corepresentations of a quantum group in the sense of Kustermans and Vaes. As a consequence, the modular autmorphism group of a unimodular quantum group can be expressed in terms of matrix coefficients. As an application, we determine the Duflo-Moore operators for the quantum group analogue of the normaliser of SU(1,1) in SL(2,C).
Keywords: Locally compact quantum groups, Orthogonality relations, Duflo-Moore operators, Modular automorphism group, Plancherel measure.
MSC: 20G42, 47D03, 47A67
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