Irreducible quantum group modules with finite dimensional weight spaces. I

Dennis Hasselstrøm Pedersen

paper

Irreducible quantum group modules with finite dimensional weight spaces. I

arXiv:1504.07042

Abstract

In this paper we classify all simple weight modules for a quantum group $U_{q}$ at a complex root of unity $q$ when the Lie algebra is not of type $G_{2}$ . By a weight module we mean a finitely generated $U_{q}$ -module which has finite dimensional weight spaces and is a sum of those. Our approach follows the procedures used by S. Fernando and O. Mathieu to solve the corresponding problem for semisimple complex Lie algebras.

37 pages