Exotic t-structures for two-block Springer fibers

We study the exotic t-structure on D_n, the derived category of coherent sheaves on the Springer fiber for a two-block nilpotent (i.e. for a nilpotent matrix of type (m+n, n) in type A). Exotic t-structures were introduced by Bezrukavnikov and Mirkovic in order to study representations of Lie algebras in positive characteristic. Using work of Cautis and Kamnitzer, we construct functors between these categories D_n, indexed by affine tangles. We use these functors to enumerate the irreducibles in the heart of D_n by crossingless matchings, and compute the Ext’s between these irreducibles. This is joint with R. Anno.