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arXiv · 1605.00866

Comparison of unitary duals of Drinfeld doubles and complex semisimple Lie groups

Yuki Arano
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Abstract

We determine a substantial part of the unitary representation theory of the Drinfeld double of a $q$-deformation of a compact Lie group in terms of the complexification of the compact Lie group. Using this, we show that the dual of every $q$-deformation of a higher rank compact Lie group has central property ${\rm (T)}$. We also determine the unitary dual of $SL_q(n,\mathbb{C})$.

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Yuki Arano. 2016-05-03. Comparison of unitary duals of Drinfeld doubles and complex semisimple Lie groups. https://doi.org/10.1007/s00220-016-2704-x

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