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CMM formula as superintegrability property of unitary model

High Energy Physics - Theory 2024-12-31 v2 Mathematical Physics math.MP

Abstract

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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Cite

@article{arxiv.2410.03175,
  title  = {CMM formula as superintegrability property of unitary model},
  author = {A. Mironov and A. Morozov and A. Popolitov},
  journal= {arXiv preprint arXiv:2410.03175},
  year   = {2024}
}

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12 pages