Unitary spherical representations of Drinfeld doubles

Yuki Arano

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arXiv · 1410.6238

Unitary spherical representations of Drinfeld doubles

Yuki Arano

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Abstract

We study irreducible spherical unitary representations of the Drinfeld double of a $q$-deformation of a connected simply connected compact Lie group, which can be considered as a quantum analogue of the complexification of the Lie group. In the case of $SU_q(3)$, we give a complete classification of such representations. As an application, we show the Drinfeld double of the quantum group $SU_q(2n+1)$ has property (T), which also implies central property (T) of the dual of $SU_q(2n+1)$.

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Yuki Arano. 2014-10-23. Unitary spherical representations of Drinfeld doubles. https://arxiv.org/abs/1410.6238

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