Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials
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 Macdona...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/214198 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials. Jasper Stokman. SIGMA 21 (2025), 086, 42 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730461727424512 |
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| author | Stokman, Jasper |
| author_facet | Stokman, Jasper |
| citation_txt | Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials. Jasper Stokman. SIGMA 21 (2025), 086, 42 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 -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.
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| first_indexed | 2026-03-21T19:10:43Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-214198 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T19:10:43Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Stokman, Jasper 2026-02-20T08:01:25Z 2025 Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials. Jasper Stokman. SIGMA 21 (2025), 086, 42 pages 1815-0659 2020 Mathematics Subject Classification: 33D80; 20C08 arXiv:2405.10609 https://nasplib.isofts.kiev.ua/handle/123456789/214198 https://doi.org/10.3842/SIGMA.2025.086 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 -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. I thank Siddhartha Sahi and Vidya Venkateswaran for several interesting discussions about the topic of the paper. I also thank the referees for their thoughtful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials Article published earlier |
| spellingShingle | Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials Stokman, Jasper |
| title | Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials |
| title_full | Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials |
| title_fullStr | Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials |
| title_full_unstemmed | Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials |
| title_short | Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials |
| title_sort | quasi-polynomial extensions of nonsymmetric macdonald-koornwinder polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214198 |
| work_keys_str_mv | AT stokmanjasper quasipolynomialextensionsofnonsymmetricmacdonaldkoornwinderpolynomials |