2024/12/31 by Gillespie, Maria, Gorsky, Eugene, Griffin, Sean T. · 1 citation
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2501.00197
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.