Monodromy free Schrödinger operators and affine $\mathfrak{sl}_2$ master functions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918531678863360 |
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| author | Grigorev, Andrei Mukhin, Evgeny |
| author_facet | Grigorev, Andrei Mukhin, Evgeny |
| contents | Given a non-zero polynomial $P(x)$, we study Fuchsian differential operators of the form $L=\partial_x^2-u(x)$ such that for all $λ\in\mathbb{C}$ the operator $L+λP(x)$ is monodromy free. We prove that all such operators are obtained from populations of critical points of ${\widehat{\mathfrak{sl}}_2}$ master functions. Moreover, we show that the reproduction procedure of critical points corresponds to a Darboux transformation of operator $P^{-1}(x)L$. As a result, we obtain a classification of all operators $L$ with such properties in the case of $P(x)=x^k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30164 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monodromy free Schrödinger operators and affine $\mathfrak{sl}_2$ master functions Grigorev, Andrei Mukhin, Evgeny Quantum Algebra Mathematical Physics Given a non-zero polynomial $P(x)$, we study Fuchsian differential operators of the form $L=\partial_x^2-u(x)$ such that for all $λ\in\mathbb{C}$ the operator $L+λP(x)$ is monodromy free. We prove that all such operators are obtained from populations of critical points of ${\widehat{\mathfrak{sl}}_2}$ master functions. Moreover, we show that the reproduction procedure of critical points corresponds to a Darboux transformation of operator $P^{-1}(x)L$. As a result, we obtain a classification of all operators $L$ with such properties in the case of $P(x)=x^k$. |
| title | Monodromy free Schrödinger operators and affine $\mathfrak{sl}_2$ master functions |
| topic | Quantum Algebra Mathematical Physics |
| url | https://arxiv.org/abs/2605.30164 |