Derived functors between cotangent bundles of flag varieties

This is a joint work with Rina Anno (U Chicago). We show how to construct a network of functors which correspond to `generalized braid diagrams', between derived categories of coherent sheaves on cotangent bundles of full and partial flag varieties. For a subclass of these diagrams (which includes all the ordinary braids) we prove that isotopic diagrams correspond to isomorphic functors. We then outline our strategy for proving the general case.