Inhomogeneous $q$-Whittaker polynomials II: ring theorem and positive specializations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917491154878464 |
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| author | Gunna, Ajeeth Yeliussizov, Damir |
| author_facet | Gunna, Ajeeth Yeliussizov, Damir |
| contents | We study inhomogeneous $q$-Whittaker polynomials which extend both $q$-Whittaker and stable Grothendieck polynomials. We prove that inhomogeneous $q$-Whittaker polynomials (in countably many variables) form a basis of certain commutative ring extending the ring of symmetric functions to a subring of its completion. We then describe positive specializations of that ring and relate them with a subset of Macdonald-positive specializations of the ring of symmetric functions. We also show some related probability distributions obtained from positive specializations of inhomogeneous $q$-Whittaker polynomials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_13432 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inhomogeneous $q$-Whittaker polynomials II: ring theorem and positive specializations Gunna, Ajeeth Yeliussizov, Damir Combinatorics 05E05, 60C05 We study inhomogeneous $q$-Whittaker polynomials which extend both $q$-Whittaker and stable Grothendieck polynomials. We prove that inhomogeneous $q$-Whittaker polynomials (in countably many variables) form a basis of certain commutative ring extending the ring of symmetric functions to a subring of its completion. We then describe positive specializations of that ring and relate them with a subset of Macdonald-positive specializations of the ring of symmetric functions. We also show some related probability distributions obtained from positive specializations of inhomogeneous $q$-Whittaker polynomials. |
| title | Inhomogeneous $q$-Whittaker polynomials II: ring theorem and positive specializations |
| topic | Combinatorics 05E05, 60C05 |
| url | https://arxiv.org/abs/2605.13432 |