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Link to original content: https://doi.org/10.1007/s00220-016-2704-x
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Comparison of Unitary Duals of Drinfeld Doubles and Complex Semisimple Lie Groups

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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 (T). We also determine the unitary dual of \({SL_q(n,\mathbb{C})}\).

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Authors and Affiliations

  1. Department of Mathematical Sciences, the University of Tokyo, Komaba, Tokyo, 153-8914, Japan

    Yuki Arano

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  1. Yuki Arano
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Correspondence to Yuki Arano.

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Communicated by Y. Kawahigashi

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Arano, Y. Comparison of Unitary Duals of Drinfeld Doubles and Complex Semisimple Lie Groups. Commun. Math. Phys. 351, 1137–1147 (2017). https://doi.org/10.1007/s00220-016-2704-x

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