Symmetric and nonsymmetric Koornwinder polynomials in the q → 0 limit
Koornwinder polynomials are a 6-parameter BC[subscript n]-symmetric family of Laurent polynomials indexed by partitions, from which Macdonald polynomials can be recovered in suitable limits of the parameters. As in the Macdonald polynomial case, standard constructions via difference operators do not...
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| Format: | Article |
| Language: | English |
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Springer US
2016
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| Online Access: | http://hdl.handle.net/1721.1/105355 https://orcid.org/0000-0002-7968-3291 |
| _version_ | 1826191686117621760 |
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| author | Venkateswaran, Vidya |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Venkateswaran, Vidya |
| author_sort | Venkateswaran, Vidya |
| collection | MIT |
| description | Koornwinder polynomials are a 6-parameter BC[subscript n]-symmetric family of Laurent polynomials indexed by partitions, from which Macdonald polynomials can be recovered in suitable limits of the parameters. As in the Macdonald polynomial case, standard constructions via difference operators do not allow one to directly control these polynomials at q=0. In the first part of this paper, we provide an explicit construction for these polynomials in this limit, using the defining properties of Koornwinder polynomials. Our formula is a first step in developing the analogy between Hall–Littlewood polynomials and Koornwinder polynomials at q=0. In the second part of the paper, we provide a construction for the nonsymmetric Koornwinder polynomials in the same limiting case; this parallels work by Descouens–Lascoux in type A. As an application, we prove an integral identity for Koornwinder polynomials at q=0. |
| first_indexed | 2024-09-23T08:59:46Z |
| format | Article |
| id | mit-1721.1/105355 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:59:46Z |
| publishDate | 2016 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1053552022-09-30T12:44:35Z Symmetric and nonsymmetric Koornwinder polynomials in the q → 0 limit Venkateswaran, Vidya Massachusetts Institute of Technology. Department of Mathematics Venkateswaran, Vidya Koornwinder polynomials are a 6-parameter BC[subscript n]-symmetric family of Laurent polynomials indexed by partitions, from which Macdonald polynomials can be recovered in suitable limits of the parameters. As in the Macdonald polynomial case, standard constructions via difference operators do not allow one to directly control these polynomials at q=0. In the first part of this paper, we provide an explicit construction for these polynomials in this limit, using the defining properties of Koornwinder polynomials. Our formula is a first step in developing the analogy between Hall–Littlewood polynomials and Koornwinder polynomials at q=0. In the second part of the paper, we provide a construction for the nonsymmetric Koornwinder polynomials in the same limiting case; this parallels work by Descouens–Lascoux in type A. As an application, we prove an integral identity for Koornwinder polynomials at q=0. 2016-11-17T23:39:54Z 2016-11-17T23:39:54Z 2015-02 2014-08 2016-08-18T15:42:26Z Article http://purl.org/eprint/type/JournalArticle 0925-9899 1572-9192 http://hdl.handle.net/1721.1/105355 Venkateswaran, Vidya. “Symmetric and Nonsymmetric Koornwinder Polynomials in the q → 0 limit.” Journal of Algebraic Combinatorics 42.2 (2015): 331–364. https://orcid.org/0000-0002-7968-3291 en http://dx.doi.org/10.1007/s10801-015-0583-4 Journal of Algebraic Combinatorics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer Science+Business Media New York application/pdf Springer US Springer US |
| spellingShingle | Venkateswaran, Vidya Symmetric and nonsymmetric Koornwinder polynomials in the q → 0 limit |
| title | Symmetric and nonsymmetric Koornwinder polynomials in the q → 0 limit |
| title_full | Symmetric and nonsymmetric Koornwinder polynomials in the q → 0 limit |
| title_fullStr | Symmetric and nonsymmetric Koornwinder polynomials in the q → 0 limit |
| title_full_unstemmed | Symmetric and nonsymmetric Koornwinder polynomials in the q → 0 limit |
| title_short | Symmetric and nonsymmetric Koornwinder polynomials in the q → 0 limit |
| title_sort | symmetric and nonsymmetric koornwinder polynomials in the q 0 limit |
| url | http://hdl.handle.net/1721.1/105355 https://orcid.org/0000-0002-7968-3291 |
| work_keys_str_mv | AT venkateswaranvidya symmetricandnonsymmetrickoornwinderpolynomialsintheq0limit |