6th December 2019: BGG resolution and sheaf cohomology of flag varieties

Nicolas Hemelsoet (UniGe) Title: BGG resolution and sheaf cohomology of flag varieties

Abstract: 

The celebrated Borel-Weil-Bott theorem gives the cohomology of homogeneous line bundles on the flag variety G/B. I will review available methods to compute cohomology of an homogeneous vector bundle and present an alternative method due to Lachowska-Qi to compute the cohomology of vector bundle on G/B, using a free U(n)-resolution of a simple finite-dimensional \g-module L(\lambda) introduced by Berstein-Gelfand-Gelfand, the BGG resolution. If we have enough time, I will present some applications we obtained recently in joint work with Rik Voorhaar.

Villa Battelle, Friday 6th December, 10:00