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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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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DOI: https://doi.org/10.1007/s00220-016-2704-x