Group algebras acting on the space of solutions of a special double confluent Heun equation

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.