"Combinatorics Related to the Springer Correspondence"

Abstract: At its heart, the Springer correspondence gives a relationship between a Lie algebra’s nilpotent orbits and the irreducible representations of its Weyl group.  The first occurrence of this relationship can be described with some basic representation theory and some linear algebra.  However, the bigger picture relies on quite a bit of geometry, combinatorics, and eventually the theory of perverse sheaves.  The goal of this talk will be to discuss an overview of Springer’s correspondence and Lusztig’s generalized Springer correspondence, with emphasis given to some of the combinatorial aspects of these results.  At the end, I will tie this to joint work with William Graham and Martha Precup.

Host: Martha Precup