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Commuting difference operators with polynomial eigenfunctions

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arxiv funct-an/9306002 v1 pith:MP4UV2LF submitted 1993-06-07 funct-an hep-thmath.OAnlin.SIsolv-int

Commuting difference operators with polynomial eigenfunctions

classification funct-an hep-thmath.OAnlin.SIsolv-int
keywords operatorsalgebracommutingdifferencesystemsaskey-wilsonassociatedcalogero-moser
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We present explicit generators of an algebra of commuting difference operators with trigonometric coefficients. The operators are simultaneously diagonalized by recently discovered q-polynomials (viz. Koornwinder's multivariable generalization of the Askey-Wilson polynomials). From the viewpoint of physics the algebra can be interpreted as consisting of the quantum integrals of a novel difference-type integrable sytem. This system generalizes the Calogero-Moser systems associated with non-exceptional root systems.

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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...