On small modules for quantum groups at roots of unity

Giovanna Carnovale, Iulian I. Simion

Published 2015-12-15Version 1

A conjecture of De Concini Kac and Procesi, proved by A. Sevostyanov in the simply-connected case, provides a bound on the minimal possible dimension of an irreducible module for quantized enveloping algebras at an odd root of unity. We pose the problem of the existence of modules whose dimension equals this bound. We show that this question cannot have a positive answer in full generality and discuss variants of this question.