DMS Algebra Seminar

Speaker: Arik Wilbert (University of South Alabama)

Title: Two-row Delta Springer varieties

Abstract: Springer fibers play an important role in geometric representation theory. These algebraic varieties naturally arise as the fibers of a resolution of singularities of the nilpotent cone and can be used to geometrically classify the irreducible representations of Weyl groups. In this talk, I will discuss the geometry and topology of a certain family of so-called Delta Springer varieties from an explicit, combinatorial point of view. These singular varieties were introduced by Griffin--Levinson--Woo in 2021 in order to give a geometric realization of an expression that appears in the t=0 case of the Delta conjecture of Haglund--Remmel--Wilson. In the two-row case, Delta Springer varieties generalize both ordinary Springer fibers as well as Kato's exotic Springer fibers. Moreover, the homology of two-row Delta Springer varieties has a diagrammatic description and can be equipped with an action of the degenerate affine Hecke algebra. This recovers and upgrades the action of the symmetric group obtained by Griffin--Levinson--Woo and yields a skein theoretic description of said action.

This is joint work with A. Lacabanne and P. Vaz.