Chennai Mathematical Institute


2.00 pm, Lecture Hall 4
Quantum analogues of cohomology of line bundles on flag manifolds

Henning Haahr Andersen
University of Aarhus, Denmark.


Some $25$ years ago Polo, Wen and I studied algebraic induction functors for quantum groups. In the right set-up their derived functors correspond to the cohomology of vector bundles on flag manifolds. We obtained quantum versions of Grothendieck vanishing, Serre duality, and Kempf's vanishing for dominant line bundles.

In this talk I will describe some of the highlights in this theory as well as some recent work and some still open problems.