Operator algebras seminar
Speaker: Hua Wang (Institut Mathématiques de Jussieu)
Title: Representations of semi-direct products of a compact quantum group with a finite group
Abstract: The main focus of this talk will be the unitary representations of semi-direct products of a compact quantum group with a finite group. In the first part, I will give a classification of all irreducible unitary representations of such quantum groups, which is merely a quantum analogue of the similar result already obtainable by the Mackey analysis in the classical group case. In the second part, I will focus on the fusion rules, i.e. what the irreducible decomposition of the tensor product of two arbitrary irreducible representations looks like. These fusion rules will be expressed by incidence numbers, which are completely determined by the representation theory of the factor quantum group, the theory of projective representations of the finite group, and a group action associated with the semi-direct product. If time permits, I will talk about some interesting special cases in which the theory can be simplified, and perhaps some applications.