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arXiv · 2410.03175

CMM formula as superintegrability property of unitary model

A. Mironov·A. Morozov·A. Popolitov
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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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A. Mironov, A. Morozov, A. Popolitov. 2024-10-04. CMM formula as superintegrability property of unitary model. https://doi.org/10.1103/physrevd.110.126026

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