Quantum analogues of cohomology of vector bundles on flag varieties

Henning Haahr Andersen

Abstract: Let $G$ be a semi-simple algebraic group with Borel subgroup $B$. The very rich geometry of the flag variety $G/B$ have been explored in many different contexts and certainly in the representation theory for $G$. For quantum groups we do not immediately have a flag variety available. In this talk we introduce quantum analogues of the cohomology of line bundles on $G/B$ and use them to define a substitute for a quantum flag variety. We prove analogues of classical theorems of Grothendieck and Serre, and apply these to establish a quantized Borel-Weil-Bott theory. Most of the results in this talk go back to joint work with Polo and Wen.

created Fri Mar 17 16:17:09 PST 2000