Complex semisimple Lie groups can be deformed into noncompact quantum groups using the Drinfeld double construction. The resulting locally compact quantum groups show up naturally in a variety of contexts; for instance in the analysis of equivariant Poincar\’e duality for the Podle\’s sphere and the study of central property (T) for q-deformations.

In this talk I will discuss some analytical aspects of complex semisimple quantum groups. In particular, I will describe the Plancherel measure and give an explicit description of the corresponding reduced group C^*-algebras.