On the Grothendieck rings of generalized Drinfeld doubles

In this paper it is shown that any irreducible representation of a Drinfeld double D(A) of a semisimple Hopf algebra A can be obtained as an induced representation from a certain Hopf subalgebra of D(A). This generalizes a well known result concerning the irreducible representations of Drinfeld doubles of finite groups [11]. Using this description we also give a formula for the fusion rules of semisimple Drinfeld doubles. This shows that the Grothendieck rings of these Drinfeld doubles have a ring structure similar to the Grothendieck rings of Drinfeld doubles of finite groups.