Category O for quantum groups

Abstract:

Let Uq denote the quantum group corresponding to a simple complex Lie algebra g. This talk will focus on some of the important classes of Uq-modules with highest weights, e.g. simple modules, Verma modules, projective modules, indecomposable tilting modules. When q is a complex root of unity we shall see how these modules can be described via the corresponding theory for the small quantum group combined with the classical theory for $\mathfrak g$. In particular, this allows us to give a formula for the irreducible characters by combining the Kazhdan-Lusztig polynomials for the finite Weyl group with those for the affine Weyl group.

This is joint work with V.~Mazorchuk (Uppsala).