THE PLANCHEREL FORMULA FOR COMPLEX SEMISIMPLE QUANTUM GROUPS
We calculate the Plancherel formula for complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. As a consequence we obtain a concrete description of their associated reduced group C *-algebras. The main ingredients in our proof are the Bernstein-Gelfand-Gelfand complex and the Hopf trace formula.