REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: The main subject of discussion will be mysterious complexes of equivariant vector bundles on rational homogeneous varieties. In particular, these appeared during the study of derived categories of coherent sheaves. We will study thoroughly the classical Grassmannian case and some generalisation to the Lagrangian case (Grassmannian of maximal isotropic subspaces). These complexes are closely related to an even more mysterious action of cyclic groups on some special classes of Young diagrams. The action in the case of classical grassmannians can be also found looking on quantum cohomology. The Lagrangian part of the story is somehow more unexpected and abstruse. The talk is based on the paper http://arxiv.org/abs/1108.2292 and somework in progress.