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Modular properties of matrix coefficients of corepresentations of a locally compact quantum group
August 30th, 2010, Quantum groups conference (Clermont-Ferrand).
Abstract
We consider locally compact quantum groups in the von Neumann algebraic
setting as introduced by Kustermans and Vaes. We will see how the modular automorphism group of the Haar weights can be expressed in terms of matrix coefficients of corepresentations. As an application this gives a
tool to determine the Plancherel transformation for (certain) locally
compact quantum groups for which the von Neumann algebra is type I.
We also define a distinguished L^p-Fourier transform for p between 1 and 2 and see how this is related to the Plancherel transformation.
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