2026/06/08 by Maria Gillespie, Eugene Gorsky, Sean T. Griffin
Mathematics · #Mathematics and Applications
paper · doi:10.1016/j.aim.2026.111087
We introduce a variety Yn,k, which we call the affine Δ-Springer fiber, generalizing the affine Springer fiber studied by Hikita, whose Borel-Moore homology has an Sn action and a bigrading that corresponds to the Delta Conjecture symmetric function revq ωΔ'_ek-1en under the Frobenius character map. We similarly provide a geometric interpretation for the Rational Shuffle Theorem in the integer slope case (km,k). The variety Yn,k has a map to the affine Grassmannian whose fibers are the Δ-Springer fibers introduced by Levinson, Woo, and the third author. Part of our proof of our geometric realization relies on our previous work on a Schur skewing operator formula relating the Rational Shuffle Theorem to the Delta Conjecture.