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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 061, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.061 (Mi sigma1360) 		 
This article is cited in 14 scientific papers (total in 14 papers)

On $q$-Deformations of the Heun Equation

Kouichi Takemura

Department of Mathematics, Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku Tokyo 112-8551, Japan
Full-text PDF (360 kB) Citations (14)
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DOI: https://doi.org/10.3842/SIGMA.2018.061
URL: https://www.imath.kiev.ua/~sigma/2018/061
Abstract: 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 its variants. Namely we investigate finite-dimensional subspaces which are invariant under the action of the $q$-Heun operator or variants of the $q$-Heun operator.
Keywords: Heun equation; $q$-deformation; regular singularity; quasi-exact solvability; degeneration.
Funding agency Grant number
Japan Society for the Promotion of Science JP26400122
He is supported by JSPS KAKENHI Grant Number JP26400122.
Received: January 18, 2018; in final form May 29, 2018; Published online June 18, 2018
Bibliographic databases:
Document Type: Article
MSC: 39A13; 33E10
Language: English
Citation: Kouichi Takemura, “On $q$-Deformations of the Heun Equation”, SIGMA, 14 (2018), 061, 16 pp.
Citation in format AMSBIB
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