Inhomogeneous $q$-Whittaker Polynomials I: Duality and Expansions
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911301599494144 |
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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 |