A skewing formula and geometric interpretation for the Rise Delta Theorem

by Sean Griffin (Universität Wien)

Thursday Dec 5, 2024, 2:30 PM → 3:30 PM Europe/Rome

Aula Seminari

In this talk, I will explain how the Delta Theorem can be obtained from the Rational Shuffle Theorem via a simple Schur skewing identity relating the two. We give two proofs of the identity: one algebraic which follows from work of Blasiak et al., and another which is combinatorial and involves a sign-reversing involution on word parking functions. I will then explain how the skewing formula can be used to give a geometric interpretation for the Delta Theorem in terms of the Borel-Moore homology of an affine Borho-MacPherson variety. Along the way, we give a new geometric interpretation of the Rational Shuffle Theorem in terms of affine Springer fibers. Joint work with Maria Gillespie and Eugene Gorsky.