Group Analysis of Differential Equations and Integrable Systems − 2018
(Chuo University, Tokyo, Japan)
On $q$-deformations of the Heun equation
The $q$-Heun equation and its variants arise as degenerations of
Ruijsenaars-van Diejen operators with one particle.
We investigate local properties of these equations.
In particular we characterize the variants of the $q$-Heun equation by
using analysis of regular singularities.
We also consider the quasi-exact solvability of the $q$-Heun equation and
Namely we investigate finite-dimensional subspaces which are invariant
under the action of the $q$-Heun operator or variants of the $q$-Heun
This is based on arXiv:1712.09564[math.CA].