Journal of Lie Theory

no. 4
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
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 
@article{JOLT_2011_21_4_a8,
     author = {M. Caspers and E. Koelink},
     title = {Modular {Properties} of {Matrix} {Coefficients} of {Corepresentations} of a {Locally} {Compact} {Quantum} {Group}},
     journal = {Journal of Lie Theory},
     pages = {905--928},
     year = {2011},
     volume = {21},
     number = {4},
     doi = {10.5802/jolt.655},
     zbl = {1266.46056},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.655/}
}
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M. Caspers; E. 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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