The Delta conjecture and Springer fibers

Abstract: The Delta Conjecture, which was very recently proven by D'Adderio--Mellit and Blasiak et al., gives a combinatorial formula for the result of applying a certain Macdonald eigenoperator to an elementary symmetric function. Pawlowski and Rhoades gave a geometric meaning to the t=0 case of this symmetric function when they introduced the space of spanning line arrangements. In this talk, I will introduce a new family of varieties, similar to the type A Springer fibers, that also give geometric meaning to the t=0 case of the Delta Conjecture. Furthermore, we will see how these new varieties lead to an LLT-type formula, and to a generalization of the Springer correspondence to the setting of induced Specht modules. If time permits, I will show how infinite unions of these varieties are related to the scheme of diagonal "rank deficient" matrices.

algebraic geometry

Audience: researchers in the topic

UC Davis algebraic geometry seminar