University of Sydney Algebra Seminar
Abel Lacabanne
Friday 9 August, 12-1pm, Place: Carslaw 275
Two-row Delta Springer varieties and representations of the degenerate affine Hecke algebra
Delta Springer varieties were recently introduced by Griffin--Lewinson--Woo to provide a geometric setting for a conjecture of Haglund--Remmel--Wilson on certain symmetric functions. These varieties are defined using a partition of an integer, and in this talk, I will focus on the case of two-row partitions. It turns out that the geometry of these two-row Delta Springer varieties has a nice diagrammatic interpretation using a variant of crossingless matchings. Griffin--Lewinson--Woo also constructed an action of the symmetric group on the top degree cohomology of Delta Springer varieties. In the two-row case, I will give a skein-theoretic interpretation of this action, and enhance it to an action of the degenerate affine Hecke algebra. These representations can also be retrived via the action of the Lie algebra sl2 on some tensor space.
This is joint work with Pedro Vaz and Arik Wilbert.