Regular representations of the quantum groups at roots of unity

Abstract

We study the bimodule structure of the quantum function algebra at roots of 1 and prove that it admits an increasing filtration with factors isomorphic to the tensor products of the dual of Weyl modules $V_\lambda^* \otimes V_{- \omega_0 \lambda}^*$. As an application we compute the 0-th Hochschild cohomology of the function algebra at roots of 1.