On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians
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| Format: | Preprint |
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2024
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| _version_ | 1866929754843643904 |
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| author | Mironov, A. Morozov, A. Popolitov, A. |
| author_facet | Mironov, A. Morozov, A. Popolitov, A. |
| contents | Quite some years ago, Oleg Chalykh has built a nice theory from the observation that the Macdonald polynomial reduces at $t=q^{-m}$ to a sum over permutations of simpler polynomials called Baker-Akhiezer functions, which can be unambiguously constructed from a system of linear difference equations. Moreover, he also proposed a generalization of these polynomials to the twisted Baker-Akhiezer functions. Recently, in a private communication Oleg suggested that these twisted Baker-Akhiezer functions could provide eigenfunctions of the commuting Hamiltonians associated with the $(-1,a)$ rays of the Ding-Iohara-Miki algebra. In the paper, we discuss this suggestion and some evidence in its support. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_10685 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians Mironov, A. Morozov, A. Popolitov, A. High Energy Physics - Theory Mathematical Physics Quantum Algebra Quite some years ago, Oleg Chalykh has built a nice theory from the observation that the Macdonald polynomial reduces at $t=q^{-m}$ to a sum over permutations of simpler polynomials called Baker-Akhiezer functions, which can be unambiguously constructed from a system of linear difference equations. Moreover, he also proposed a generalization of these polynomials to the twisted Baker-Akhiezer functions. Recently, in a private communication Oleg suggested that these twisted Baker-Akhiezer functions could provide eigenfunctions of the commuting Hamiltonians associated with the $(-1,a)$ rays of the Ding-Iohara-Miki algebra. In the paper, we discuss this suggestion and some evidence in its support. |
| title | On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2410.10685 |