Chennai Mathematical Institute


3.30 pm, Seminar Hall
Fernando-Mathieu classification of simple weight modules for quantum groups

Dennis Hasselstrom Pedersen
University of Aarhus, Denmark.


Let $U$ be the universal enveloping algebra of a Lie algebra. Consider the category of Lie algebra modules that consists of modules that are finitely generated as $U$ modules, split up into weight spaces and have all weight spaces finite dimensional. The BGG category ${\cal O}$ is a full subcategory of this category. We want to consider the simple modules of this category. S. L. Fernando showed in his paper "Lie Algebra Modules with Finite Dimensional Weight Spaces, I" that the classification of simple modules reduces to a classification of simple modules and so-called torsion free modules. O. Mathieu finished the classification by classifying all torsion free modules.

For quantum groups at a non root of unity the theory is very similar. I will show how to reduce the problem to the classification of torsion free modules and if time permits talk about the differences in the root of unity case.