A $3\times3$ linear $q$-difference system with $E_8^{(1)}$-symmetry
Quantum Algebra
2026-01-13 v1
Abstract
We present a linear -difference equation of rank , which admits the affine Weyl group symmetry of type . We further compare this equation with Moriyama-Yamada's quantum curve which has -symmetry. The symmetry of our equation is provided by the -middle convolution, defined by Sakai-Yamaguchi and reformulated by Arai-Takemura. In this paper, we provide a reconstruction of the -middle convolution via a -Okubo type equation.
Keywords
Cite
@article{arxiv.2601.06070,
title = {A $3\times3$ linear $q$-difference system with $E_8^{(1)}$-symmetry},
author = {Takahiko Nobukawa},
journal= {arXiv preprint arXiv:2601.06070},
year = {2026}
}
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34 pages