Hunter Spink (Mar. 25, 2022):  A new Chern character for "classical Lie type" combinatorics
Channel: Algebraic Geometry at Stanford
Date: 2022-03-26

For X of “classical Lie type” (formally such that X has a GKM torus action where all characters are of the form t_i, t_i+t_j, and t_i-t_j for various i,j), we adapt for combinatorial applications the (equivariant) Hirzebruch-Riemann-Roch framework which computes Euler characteristics of vector bundles via cohomological computations, extending previous joint work in type A with Andrew Berget, Chris Eur, and Dennis Tseng.

This framework directly relates the structure sheaf of Schubert varieties to Grothendieck polynomials, produces formulas (some of them new) relating the number of lattice points and volumes for type A and B generalized permutahedrons, and when applied to ample equivariant vector bundles on toric varieties is a key component in recent progress on establishing and unifying results on the log-concavity of sequences associated to matroids and delta-matroids.

[This is joint work with Chris Eur, Alex Fink, and Matthew Larson.]