Modular properties of matrix coefficients of corepresentations of a locally compact quantum group

Details Modular properties of matrix coefficients of corepresentations of a locally compact quantum group Modular properties of matrix coefficients of corepresentations of a locally compact quantum group

2010-03-11

arxiv.org/abs/1003.2278v2

Journal of Lie Theory 21 (2011), no. 4, 905-928

Mathematics

Operator Algebras

22 pages. To appear in Journal of Lie Theory

Scientific paper

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 $SL(2,\mathbb{C}$).

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