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The combinatorics of 2-row Springer fibers in type D

Algebra & Discrete Mathematics

Speaker: Catharina Stroppel, Universitaet Bonn and University of Chicago
Location: 1147 MSB
Start time: Mon, Oct 1 2012, 4:10PM

Given a nilpotent endomorphism N of some finite dimensional vector space V we can consider the space of all full flags in V fixed under N. This is the Springer fiber of type A. It plays a very prominent role in geometric representation theory. The construction generalizes to all other semi-simple Lie groups. The combinatorics of irreducible components is reasonably well understood in type A, but almost nothing is known in other types. I want to treat in detail the case for type D,B,C where the nilpotent has two Jordan blocks. The geometry will then be described in terms of domino tableaux following the classical approach, but then also in terms of a new diagram combinatorics which can be related to crystals and Kazhdan-Lusztig polynomials.