CMM formula as superintegrability property of unitary model
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912171116462080 |
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| author | Mironov, A. Morozov, A. Popolitov, A. |
| author_facet | Mironov, A. Morozov, A. Popolitov, A. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_03175 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | CMM formula as superintegrability property of unitary model Mironov, A. Morozov, A. Popolitov, A. High Energy Physics - Theory Mathematical Physics 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. |
| title | CMM formula as superintegrability property of unitary model |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2410.03175 |