Combinatorics Seminar: Character formulas from Lusztig varieties and affine Springer fibers

Abstract: Goresky–Kottwitz–MacPherson, studying an analogue of the Springer resolution for loop groups, showed that the equivariant cohomology of an affine Springer fiber can be decomposed into that of parabolic, yet classical, Hessenberg varieties. We conjecture a formula for the Springer action on the total cohomology, inspired by a parallel formula that we can establish in the setting of braid-theoretic Lusztig varieties. The latter is in turn motivated by a knot-theoretic invariant called the HOMFLY-PT polynomial and its algebro-geometric construction. If time permits, we will discuss how these formulas relate to a recent preprint of Ram.

Host: Martha Precup