Séminaire Lotharingien de Combinatoire, 89B.31 (2023), 12 pp.
Byung-Hak Hwang, Jihyeug Jang, Jang Soo Kim,
Minho Song and U-Keun Song
Refined Canonical Stable Grothendieck Polynomials and Their Duals
Abstract.
In this extended abstract we introduce refined canonical stable Grothendieck polynomials
and their duals with two infinite sequences of parameters. These
polynomials unify several generalizations of Grothendieck polynomials
including canonical stable Grothendieck polynomials due to Yeliussizov,
refined Grothendieck polynomials due to Chan and Pflueger, and refined dual
Grothendieck polynomials due to Galashin, Liu, and Grinberg. We give
Jacobi--Trudi-like formulas, combinatorial models, Schur expansions, Schur
positivity, and dualities of these polynomials. We also consider flagged
versions of Grothendieck polynomials and their duals with skew shapes.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
The following versions are available: