English

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

Quantum Algebra 2026-01-13 v1

Abstract

We present a linear qq-difference equation of rank 33, which admits the affine Weyl group symmetry of type E8(1)E_8^{(1)}. We further compare this equation with Moriyama-Yamada's quantum curve which has W(E8(1))W(E_8^{(1)})-symmetry. The symmetry of our equation is provided by the qq-middle convolution, defined by Sakai-Yamaguchi and reformulated by Arai-Takemura. In this paper, we provide a reconstruction of the qq-middle convolution via a qq-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}
}

Comments

34 pages

R2 v1 2026-07-01T08:58:09.424Z