The symmetry algebra of the Smorodinsky-Winternitz II system is identified as the Laguerre-Heun algebra through explicit operators Y, W and their commutation relations.
Tridiagonalization and the Heun equation
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
fields
math-ph 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
The 2D Smorodinsky--Winternitz II system and the Laguerre--Heun algebra
The symmetry algebra of the Smorodinsky-Winternitz II system is identified as the Laguerre-Heun algebra through explicit operators Y, W and their commutation relations.