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20 November Friday

Travis Scrimshaw (University of Queensland): Coloring K-Theoretic Schubert Calculus

20 November 2020, 17:00 - 20 November 2020, 18:00
En ligne/online, Canada

Résumé: Double Grothendieck polynomials were introduced as polynomial
representatives of Schubert varieties in the equivariant K-theory ring
of the full flag variety. Recently, a combinatorial formula using
bumpless pipe dreams of Lam-Lee-Shimozono was proven by Weigandt using a
formula due to Lascoux that describes double Grothendieck polynomials
using alternating sign matrices. In this talk, we will give another
proof of this formula by translating bumpless pipe dreams into the
language of colored integrable vertex models. We then show the
generating function (aka the partition function) of our colored lattice
model satisfies the same functional relations as double Grothendiecks up
to a known factor by using the Yang-Baxter equation. By exploiting a
natural duality, we use our vertex model to give a new proof that double
Grothendieck polynomials for vexillary permutations are flagged
Grothenieck polynomials and that the stable limit is a factorial
Grothendieck polynomial. This is joint work with Valentin Buciumas.

Details
Date: 20 November 2020
Time: 17 h 00 min - 18 h 00 min
Venue
Venue Name: En ligne/online
Address: Canada