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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 |
Description
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.