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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2503.18057 |
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| _version_ | 1866913753939836928 |
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| author | Rains, Eric Rosengren, Hjalmar |
| author_facet | Rains, Eric Rosengren, Hjalmar |
| contents | We prove that the Ruijsenaars model admits a one-parameter commuting family of Q-operators. The commutativity is equivalent to an elliptic hypergeometric integral transformation that was conjectured by Gadde et al., and has an alternative interpretation in terms of S-duality for quiver gauge theories. We present two proofs of this conjecture, one using the elliptic Macdonald polynomials of Langmann et al., and one using known results on elliptic hypergeometric integrals. We also explain how the Noumi-Sano operators appear as degenerations of Q-operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18057 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Q-operators for the Ruijsenaars model Rains, Eric Rosengren, Hjalmar Mathematical Physics Classical Analysis and ODEs Exactly Solvable and Integrable Systems We prove that the Ruijsenaars model admits a one-parameter commuting family of Q-operators. The commutativity is equivalent to an elliptic hypergeometric integral transformation that was conjectured by Gadde et al., and has an alternative interpretation in terms of S-duality for quiver gauge theories. We present two proofs of this conjecture, one using the elliptic Macdonald polynomials of Langmann et al., and one using known results on elliptic hypergeometric integrals. We also explain how the Noumi-Sano operators appear as degenerations of Q-operators. |
| title | Q-operators for the Ruijsenaars model |
| topic | Mathematical Physics Classical Analysis and ODEs Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2503.18057 |