Inhomogeneous $q$-Whittaker Polynomials I: Duality and Expansions

Fuente: arXiv
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Main Authors: Gunna, Ajeeth, Wheeler, Michael, Zinn-Justin, Paul
Format: Preprint
Published: 2025
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author Gunna, Ajeeth
Wheeler, Michael
Zinn-Justin, Paul
author_facet Gunna, Ajeeth
Wheeler, Michael
Zinn-Justin, Paul
contents We introduce a new family of symmetric polynomials $\mathfrak{G}^{(\mathbf{u},\mathbf{v})}_λ$ arising from exactly solvable lattice models associated with the quantised loop algebra $\mathcal{U}_{q}(\mathfrak{sl}_{2}[z^\pm])$. The polynomials $\mathfrak{G}^{(\mathbf{u},\mathbf{v})}_λ$ unify $q$-Whittaker polynomials, inhomogeneous $q$-Whittaker polynomials, Grothendieck polynomials and their duals. Using Yang--Baxter equation, we derive Cauchy identities and combinatorial formulas for the transition coefficients.
format Preprint
id arxiv_https___arxiv_org_abs_2512_04468
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Inhomogeneous $q$-Whittaker Polynomials I: Duality and Expansions
Gunna, Ajeeth
Wheeler, Michael
Zinn-Justin, Paul
Combinatorics
Mathematical Physics
05E05
We introduce a new family of symmetric polynomials $\mathfrak{G}^{(\mathbf{u},\mathbf{v})}_λ$ arising from exactly solvable lattice models associated with the quantised loop algebra $\mathcal{U}_{q}(\mathfrak{sl}_{2}[z^\pm])$. The polynomials $\mathfrak{G}^{(\mathbf{u},\mathbf{v})}_λ$ unify $q$-Whittaker polynomials, inhomogeneous $q$-Whittaker polynomials, Grothendieck polynomials and their duals. Using Yang--Baxter equation, we derive Cauchy identities and combinatorial formulas for the transition coefficients.
title Inhomogeneous $q$-Whittaker Polynomials I: Duality and Expansions
topic Combinatorics
Mathematical Physics
05E05
url https://arxiv.org/abs/2512.04468