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Nonsymmetric Koornwinder polynomials and duality

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arxiv q-alg/9710032 v2 pith:5CENLARQ submitted 1997-10-27 q-alg math.QA

Nonsymmetric Koornwinder polynomials and duality

classification q-alg math.QA
keywords koornwinderpolynomialsmacdonaldalgebradiejendualitynonsymmetricwork
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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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Cited by 2 Pith papers

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  1. Quantized Coulomb branch of 4d $\mathcal{N}=2$ $Sp(N)$ gauge theory and spherical DAHA of $(C_N^{\vee}, C_N)$-type

    hep-th 2025-03 unverdicted novelty 7.0

    Quantized Coulomb branch of 4d N=2 Sp(N) theory with given matter content matches spherical DAHA of (C_N^vee, C_N) type, proven for N=1 and conjectured for higher N with 't Hooft loop evidence.

  2. Integrable systems inspired by DAHA and DIM algebra: type $C^\vee C$ versus type $A$

    hep-th 2026-07 accept novelty 4.5

    Type C∨C DAHA and Koornwinder systems mirror type-A Macdonald structures for Hamiltonians, recursions, evaluations and dualities, but lack a usable Noumi-Shiraishi-style universal series and SL(2,Z)-type twisting auto...