Comparison of unitary duals of Drinfeld doubles and complex semisimple Lie groups (Q521987)

In this paper it is shown that quantum Harish-Chandra modules for a certain \(q\)-deformation of a complex semisimple Lie group can be seen as admissible representations for the Drinfeld double of this \(q\)-deformation. This is used to determine a substantial part of the unitary representation theory of the Drinfeld double in question. As an application, the unitary dual of \(\mathrm{SL}_q(n,\mathbb{C})\) is determined.