On q-deformations of Heun equation

Kouichi Takemura, Chuo University, Tokyo. Part of the Integrable Systems seminar series.

The q-Heun equation and its variants were obtained by degenerations of Ruijsenaars-van Diejen operators with one particle.

We investigate local properties of these equations. Especially we characterize the variants of q-Heun equation by using analysis of regular singularities.

We also consider quasi-exact solvability of the q-Heun equation and its variants. Namely we investigate finite-dimensional subspaces which are invariant under the action of the q-Heun operator or the variants of q-Heun operator.

This talk is based on arXiv:1712.09564.