$c$-functions and Koornwinder polynomials
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929561147539456 |
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| author | Colmenarejo, Laura Ram, Arun |
| author_facet | Colmenarejo, Laura Ram, Arun |
| contents | This paper develops the theory of Macdonald-Koornwinder polynomials in parallel analogy with the work done for the $GL_n$ case in [CR22]. In the context of the type $CC_n$ affine root system the Macdonald polynomials of other root systems of classical type are specializations of the Koornwinder polynomials. We derive $c$-function formulas for symmetrizers and use them to give $E$-expansions, principal specializations and norm formulas for bosonic, mesonic and fermionic Koornwinder polynomials. Finally, we explain the proof of the norm conjectures and constant term conjectures for the Koornwinder case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19957 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $c$-functions and Koornwinder polynomials Colmenarejo, Laura Ram, Arun Combinatorics 05E05 (Primary), 33D52 (Secondary) This paper develops the theory of Macdonald-Koornwinder polynomials in parallel analogy with the work done for the $GL_n$ case in [CR22]. In the context of the type $CC_n$ affine root system the Macdonald polynomials of other root systems of classical type are specializations of the Koornwinder polynomials. We derive $c$-function formulas for symmetrizers and use them to give $E$-expansions, principal specializations and norm formulas for bosonic, mesonic and fermionic Koornwinder polynomials. Finally, we explain the proof of the norm conjectures and constant term conjectures for the Koornwinder case. |
| title | $c$-functions and Koornwinder polynomials |
| topic | Combinatorics 05E05 (Primary), 33D52 (Secondary) |
| url | https://arxiv.org/abs/2410.19957 |