Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915555115532288 |
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| author | Stokman, Jasper |
| author_facet | Stokman, Jasper |
| contents | In a recent joint paper with S. Sahi and V. Venkateswaran (2025), families of actions of the double affine Hecke algebra on spaces of quasi-polynomials were introduced. These so-called quasi-polynomial representations led to the introduction of quasi-polynomial extensions of the nonsymmetric Macdonald polynomials, which reduce to metaplectic Iwahori-Whittaker functions in the $\mathfrak{p}$-adic limit. In this paper, these quasi-polynomial representations are extended to Sahi's 5-parameter double affine Hecke algebra, and the quasi-polynomial extensions of the nonsymmetric Koornwinder polynomials are introduced. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10609 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials Stokman, Jasper Representation Theory 20C08, 33D52 In a recent joint paper with S. Sahi and V. Venkateswaran (2025), families of actions of the double affine Hecke algebra on spaces of quasi-polynomials were introduced. These so-called quasi-polynomial representations led to the introduction of quasi-polynomial extensions of the nonsymmetric Macdonald polynomials, which reduce to metaplectic Iwahori-Whittaker functions in the $\mathfrak{p}$-adic limit. In this paper, these quasi-polynomial representations are extended to Sahi's 5-parameter double affine Hecke algebra, and the quasi-polynomial extensions of the nonsymmetric Koornwinder polynomials are introduced. |
| title | Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials |
| topic | Representation Theory 20C08, 33D52 |
| url | https://arxiv.org/abs/2405.10609 |