Chennai Mathematical Institute


3.30. pm, Seminar Hall
Tilting modules for algebraic groups and quantum groups

Henning Haahr Andersen
University of Aarhus, Denmark.


Let $V$ be a finite dimensional vector space over a field of characteristic $p>0$ and set $G = GL(V)$. A natural question is then to describe the decomposition of the tensor powers $V^{\otimes r}$ into indecomposable summands for $G$. This is a very hard problem whose solution is not known except when the dimension of $V$ is at most $2$.

The summands occurring in this decomposition are the tilting modules for $G$. In this talk I shall present some of the recent theory on tilting modules for an arbitrary reductive algebraic group over $k$. Special emphasis will be on results related to the above mentioned problem.

In the case where $G$ is replaced by the corresponding quantum group $G_q$ with $q$ being a complex root of unity we shall describe the solution by W. Soergel of how to decompose tensor powers of the natural representation $V_q$ of $G_q$.