Nested ansatz method for Baker-Akhiezer functions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917220786896896 |
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| author | Mironov, A. Morozov, A. Popolitov, A. |
| author_facet | Mironov, A. Morozov, A. Popolitov, A. |
| contents | We explain that the logic behind the derivation of the Noumi-Shiraishi function can be applied directly to the Baker-Akhiezer function (BAF). This amounts to changing an ansatz for BAF to a nested one, where the BAF of N + 1 variables is recursively expressed as a sum over BAFs of N variables. This may be seen as a generalization of symmetrization trick from [1], but for the generally non-symmetric BAF. We demonstrate that, for usual non-twisted (a = 1) BAFs, this method correctly reproduces the Noumi-Shiraishi formula directly from linear equations, resolving the ambiguity related to non-simple roots. For the first non-trivial twisted case (N = 3, a = 2) this method also fixes this ambiguity, moreover, answers for the first few layers of coefficients are in the form of direct quantization of [1]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17453 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nested ansatz method for Baker-Akhiezer functions Mironov, A. Morozov, A. Popolitov, A. High Energy Physics - Theory Mathematical Physics Combinatorics Quantum Algebra We explain that the logic behind the derivation of the Noumi-Shiraishi function can be applied directly to the Baker-Akhiezer function (BAF). This amounts to changing an ansatz for BAF to a nested one, where the BAF of N + 1 variables is recursively expressed as a sum over BAFs of N variables. This may be seen as a generalization of symmetrization trick from [1], but for the generally non-symmetric BAF. We demonstrate that, for usual non-twisted (a = 1) BAFs, this method correctly reproduces the Noumi-Shiraishi formula directly from linear equations, resolving the ambiguity related to non-simple roots. For the first non-trivial twisted case (N = 3, a = 2) this method also fixes this ambiguity, moreover, answers for the first few layers of coefficients are in the form of direct quantization of [1]. |
| title | Nested ansatz method for Baker-Akhiezer functions |
| topic | High Energy Physics - Theory Mathematical Physics Combinatorics Quantum Algebra |
| url | https://arxiv.org/abs/2601.17453 |