2024/12/29 by Adam Gregory, Zachary Hamaker, Gregory, Adam +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2412.20615
Lam, Lee and Shimozono recently introduced backstable double Grothendieck polynomials to represent K-theory classes of the infinite flag variety. They used them to define double β-Stanley symmetric functions, which expand into double stable Grothendieck functions with polynomial coefficients called double β-Edelman--Greene coefficients. Anderson proved these coefficients are β-Graham positive. For vexillary permutations, this is equivalent to a statement for skew flagged double β-Grothendieck functions. Working in this setting, we give a tableau formula for vexillary double β-Edelman--Greene coefficients that is manifestly β-Graham positive. Our formula demonstrates a finer notion of positivity than was previously known.