Tridiagonalization and the Heun equation

Abstract

It is shown that the tridiagonalization of the hypergeometric operator $L$ yields the generic Heun operator $M$. The algebra generated by the operators $L,M$ and $Z=[L,M]$ is quadratic and a one-parameter generalization of the Racah algebra. The new Racah-Heun orthogonal polynomials are introduced as overlap coefficients between the eigenfunctions of the operators $L$ and $M$. An interpretation in terms of the Racah problem for $su(1,1)$ algebras and separation of variables in a superintegrable system are discussed.

17 pages

References in corpus (2)

• One-Dimensional Quasi-Exactly Solvable Schrödinger Equations
• The Heun operator as a Hamiltonian

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