dorsal/arxiv
View SchemaNonsymmetric Koornwinder polynomials and duality
| Authors | Siddhartha Sahi |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9710032 |
| URL | https://arxiv.org/abs/q-alg/9710032 |
| Journal | Ann. of Math. (2) 150 (1999), no. 1, 267-282 |
Abstract
Motivated by the work of Koornwinder, Macdonald, Cherednik, Noumi, and van Diejen we define a 6-parameter double affine Hecke algebra and establish its basic structural properties, including the existence of an involution. We relate the algebra to (symmetric and nonsymmetric) Koornwinder polynomials via the method of intertwiners and, as a consequence, obtain a proof of Macdonald's duality conjecture for Koornwinder polynomials. Combined with earlier work of van Diejen this completely settles all the outstanding conjectures of Macdonald and Koornwinder about these polynomials.
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"abstract": "Motivated by the work of Koornwinder, Macdonald, Cherednik, Noumi, and van\nDiejen we define a 6-parameter double affine Hecke algebra and establish its\nbasic structural properties, including the existence of an involution. We\nrelate the algebra to (symmetric and nonsymmetric) Koornwinder polynomials via\nthe method of intertwiners and, as a consequence, obtain a proof of Macdonald\u0027s\nduality conjecture for Koornwinder polynomials. Combined with earlier work of\nvan Diejen this completely settles all the outstanding conjectures of Macdonald\nand Koornwinder about these polynomials.",
"arxiv_id": "q-alg/9710032",
"authors": [
"Siddhartha Sahi"
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"journal_ref": "Ann. of Math. (2) 150 (1999), no. 1, 267-282",
"title": "Nonsymmetric Koornwinder polynomials and duality",
"url": "https://arxiv.org/abs/q-alg/9710032"
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