3-4 hours of lectures per week.
Lecturer
Henning Haahr Andersen
Content
This will be a continuation of the course "Quantum groups" from the fall semester 2001. We shall study further the integrable representations of a quantum group. Of particular importance for us will be the case where the quantum parameter is specialized to a root of unity. In this case we shall prove a linkage principle which involves the orbits of the affine Weyl group attached to our quantum group.
Also in the root of unity case we shall study tilting modules. They play an important role in several contexts. We shall among other things demonstrate how they lead to a "finite" tensor category which is needed in the Reshetikhin-Turaev theory of quantum invariant for 3-manifolds.
Other possible topics: relations to characteristic p representation theory, canonical/crystal bases, Schur-Weyl duality.
Prerequisites
Quantum groups (fall 2001).
Literature
Informal notes. Articles.