REPRESENTATIONS OF QUANTUM GROUPS AT ROOTS OF 1: REDUCTION TO THE EXCEPTIONAL CASE

This paper is a continuation of the papers [DC-K] and [DC-K-P] on representations of quautum groups at roots of 1. Here we show that an irreducible representation of a quantum group at an odd root of 1 can be uniquely induced from an exceptional representation of a smaller quantum group. This reduces the classification of representations, the calculation of their characters and dimensions, etc, to the exceptional case.