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arXiv · 2601.06070

A $3\times3$ linear $q$-difference system with $E_8^{(1)}$-symmetry

Takahiko Nobukawa
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Abstract

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.

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BibTeXRIS

Takahiko Nobukawa. 2025-12-29. A $3\times3$ linear $q$-difference system with $E_8^{(1)}$-symmetry. https://arxiv.org/abs/2601.06070

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