Double orthodontia formulas and Lascoux positivity, Linus Setiabrata (University of Chicago) -- February 27th, 2025

Motivated by our search for a representation theoretic avatar for double Grothendieck polynomials G_w(x;y), we give a new formula for G_w(x;y) based on Magyar's orthodontia algorithm for diagrams. Our formula gives a curious positivity result: Writing S_w(x;y) for a vexillary double Schubert polynomial, the polynomial x_1^n\dots x_n^n S_w(x_n^{-1},\dots, x_1^{-1}; 1,\dots,1) is a graded nonnegative sum of Lascoux polynomials. Joint work with Avery St. Dizier.

The seminar co-organizers are Ian Cavey, Andrew Hardt, David Keating, and Alexander Yong.