A $3\times3$ linear $q$-difference system with $E_8^{(1)}$-symmetry
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915719653883904 |
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| author | Nobukawa, Takahiko |
| author_facet | Nobukawa, Takahiko |
| contents | We present a linear $q$-difference equation of rank $3$, which admits the affine Weyl group symmetry of type $E_8^{(1)}$. We further compare this equation with Moriyama-Yamada's quantum curve which has $W(E_8^{(1)})$-symmetry. The symmetry of our equation is provided by the $q$-middle convolution, defined by Sakai-Yamaguchi and reformulated by Arai-Takemura. In this paper, we provide a reconstruction of the $q$-middle convolution via a $q$-Okubo type equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06070 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A $3\times3$ linear $q$-difference system with $E_8^{(1)}$-symmetry Nobukawa, Takahiko Quantum Algebra 39A13 We present a linear $q$-difference equation of rank $3$, which admits the affine Weyl group symmetry of type $E_8^{(1)}$. We further compare this equation with Moriyama-Yamada's quantum curve which has $W(E_8^{(1)})$-symmetry. The symmetry of our equation is provided by the $q$-middle convolution, defined by Sakai-Yamaguchi and reformulated by Arai-Takemura. In this paper, we provide a reconstruction of the $q$-middle convolution via a $q$-Okubo type equation. |
| title | A $3\times3$ linear $q$-difference system with $E_8^{(1)}$-symmetry |
| topic | Quantum Algebra 39A13 |
| url | https://arxiv.org/abs/2601.06070 |