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CMM formula as superintegrability property of unitary model

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arxiv 2410.03175 v2 pith:H4EVBZM6 submitted 2024-10-04 hep-th math-phmath.MP

A. Mironov , A. Morozov , A. Popolitov This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords arbitraryhopflinkmacdonaldmodelpairsuperintegrabilityunitary
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A typical example of superintegrability is provided by expression of the Hopf link hyperpolynomial in an arbitrary representation through a pair of the Macdonald polynomials at special points. In the simpler case of the Hopf link HOMFLY-PT polynomial and a pair of the Schur functions, it is a relation in the unitary matrix model. We explain that the Cherednik-Mehta-Macdonald (CMM) identity for bilinear Macdonald residues with an elliptic weight function is nothing but a reformulation of these same formulas. Their lifting to arbitrary knots and links, even torus ones remains obscure.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Macdonald deformation of Vogel's universality and link hyperpolynomials

    hep-th 2025-05 conditional novelty 6.0 of 10

    For the adjoint square in ADE Lie algebras, products of Macdonald dimensions with deformed Littlewood-Richardson coefficients are universal, yielding universal formulas for T[2,2n] link hyperpolynomials.

  2. On Refined Vogel's universality

    hep-th 2025-04 conditional novelty 5.0 of 10

    For the simply laced simple Lie algebras (A_n, D_n, E_6, E_7, E_8), the adjoint Macdonald dimension is captured by one universal rational function of Vogel's parameters.

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

    hep-th 2026-07 accept novelty 4.5 of 10

    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...

  4. Chalykh's Baker-Akhiezer functions as eigenfunctions of the integer-ray integrable systems

    hep-th 2024-11 conditional novelty 4.0 of 10

    In explicit small cases, twisted Baker-Akhiezer functions satisfy the defining linear equations and are eigenfunctions of the integer-ray DIM Hamiltonians.

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