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.
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}
}
Comments
12 pages