A 3×3 linear q-difference system with E8(1)-symmetry
Abstract
We present a linear q-difference equation of rank 3, which admits the affine Weyl group symmetry of type E8(1). We further compare this equation with Moriyama-Yamada's quantum curve which has W(E8(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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.