Journal of Lie Theory

no. 4
Modular Properties of Matrix Coefficients of Corepresentations of a Locally Compact Quantum Group
Martijn Caspers1; Erik Koelink1
1Radboud Universiteit, IMAPP, Heyendaalseweg 135, Nijmegen, 6525 AJ, The Netherlands
Journal of Lie Theory, Volume 21 (2011) no. 4, pp. 905-928
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).
DOI: 10.5802/jolt.655
Classification: 20G42, 47D03, 47A67
Keywords: Locally compact quantum groups, Orthogonality relations, Duflo-Moore operators, Modular automorphism group, Plancherel measure

Martijn Caspers  1 ; Erik Koelink  1

1 Radboud Universiteit, IMAPP, Heyendaalseweg 135, Nijmegen, 6525 AJ, The Netherlands 
Martijn Caspers; Erik Koelink. Modular Properties of Matrix Coefficients of Corepresentations of a Locally Compact Quantum Group. Journal of Lie Theory, Volume 21 (2011) no. 4, pp. 905-928. doi: 10.5802/jolt.655
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     title = {Modular {Properties} of {Matrix} {Coefficients} of {Corepresentations} of a {Locally} {Compact} {Quantum} {Group}},
     journal = {Journal of Lie Theory},
     pages = {905--928},
     year = {2011},
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     number = {4},
     doi = {10.5802/jolt.655},
     zbl = {1266.46056},
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