On Spectrum Generating Algebra of the Heun Operator
Priyasri Kar, Ritesh K. Singh, Ananda Dasgupta, Prasanta K., Panigrahi

TL;DR
This paper explores the algebraic structure of the Heun operator, showing how it can be represented using an $su(1,1)$ algebra under certain conditions, and demonstrates spectrum generation with examples.
Contribution
It introduces a spectrum generating algebra for the Heun operator using $su(1,1)$ elements, revealing conditions for elementary singularities and illustrating spectrum generation.
Findings
Heun operator can be expressed via $su(1,1)$ algebra elements.
Regular singularities at 0 and infinity are elementary under certain parameters.
Spectrum generation demonstrated through specific examples.
Abstract
The Heun operator has been cast, in terms of the elements of an underlying algebra, under specific parametric conditions, for the purpose of spectrum generation. These elements are differential operators of \emph{degrees} and . It is found that the regular singularities at and of the general Heun equation must be \emph{elementary} under the required parametric conditions. The spectrum generation has been demonstrated through a set of examples.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Nonlinear Waves and Solitons · Quantum chaos and dynamical systems
