math-ph

# Title: On the dimensions of oscillator-like algebras induced by orthogonal polynomials: non-symmetric case

Abstract: There is a generalized oscillator-like algebra associated with every class of orthogonal polynomials $\{\Psi_n(x)\}_{n=0}^{\infty}$, on the real line, satisfying a four term non-symmetric recurrence relation $x\Psi_n(x)=b_n\Psi_{n+1}(x)+a_n\Psi_n(x)+b_{n-1}\Psi_{n-1}(x),~\Psi_0(x)=1,~b_{-1}=0$. This note presents necessary and sufficient conditions on $a_n$ and $b_n$ for such algebras to be of finite dimension. As examples, we discuss the dimensions of oscillator-like algebras associated with Laguerre and Jacobi polynomials.
 Subjects: Mathematical Physics (math-ph) MSC classes: 33C45 Journal reference: Rep. Math. Phys., 79 (2017), 67-79 DOI: 10.1016/S0034-4877(17)30021-6 Cite as: arXiv:1509.01293 [math-ph] (or arXiv:1509.01293v2 [math-ph] for this version)

## Submission history

From: Kengatharam Thirulogasanthar [view email]
[v1] Thu, 3 Sep 2015 22:29:47 GMT (10kb)
[v2] Fri, 8 Sep 2017 11:12:17 GMT (10kb)

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