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

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 $(\mathrm{T})$. We also determine the unitary dual of $S{L}_q(n,\mathbb{C})$.

10 pages

References in corpus (1)

• Representation theory for subfactors, $\lambda$-lattices and C*-tensor categories

Cited by in corpus (4)

• Property (T) discrete quantum groups and subfactors with triangle presentations
• Admissibility Conjecture and Kazhdan's Property (T) for quantum groups
• Quantum groups, property (T), and weak mixing
• Howe-Moore type theorems for quantum groups and rigid C*-tensor categories