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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 204, Number 2, Pages 153–170
DOI: https://doi.org/10.4213/tmf9900 (Mi tmf9900) 		 
Group algebras acting on the space of solutions of a special double confluent Heun equation

V. M. Buchstabera, S. I. Tertychnyib

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b All-Russian Scientific Research Institute for Physical and Radio-Technical Measurements (VNIIFTRI), Mendeleevo, Moscow region, Russia
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DOI: https://doi.org/10.4213/tmf9900
Abstract: We study properties of the space $\boldsymbol{\Omega}$ of solutions of a special double confluent Heun equation closely related to the model of a overdamped Josephson junction. We describe operators acting on $\boldsymbol{\Omega}$ and relations in the algebra $\mathcal{A}$ generated by them over the real number field. The structure of $\mathcal{A}$ depends on parameters. We give conditions under which $\mathcal{A}$ is isomorphic to a group algebra and describe two corresponding group structures.
Keywords: special double confluent Heun equation, monodromy operator, solution space symmetry, group algebra.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00192
This research was supported in part by the Russian Foundation for Basic Research (Grant No. 17-01-00192).
Received: 06.03.2020
Revised: 06.03.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 204, Issue 2, Pages 967–983
DOI: https://doi.org/10.1134/S0040577920080012
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. M. Buchstaber, S. I. Tertychnyi, “Group algebras acting on the space of solutions of a special double confluent Heun equation”, TMF, 204:2 (2020), 153–170; Theoret. and Math. Phys., 204:2 (2020), 967–983
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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