Irreducible quantum group modules with finite dimensional weight spaces. I
Abstract
In this paper we classify all simple weight modules for a quantum group Uq at a complex root of unity q when the Lie algebra is not of type G2. By a weight module we mean a finitely generated Uq-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.
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