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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Nobukawa, Takahiko
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915719653883904
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