Abstract: I will discuss the geometry and topology of a certain family of so-called Delta Springer varieties from an explicit, diagrammatic 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, and 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.
Two-row Delta Springer varieties
2025/05/12 (Mon.) 15:00~16:00