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arXiv · 1903.05318

$C_\lambda$- Extended oscillator algebra and $d$-orthogonal polynomials

Fethi Bouzeffour·Wissem Jedidi
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Abstract

In this paper we first construct an analytic realization of the $C_\lambda$-extended oscillator algebra with the help of difference-differential operators. Secondly, we study families of $d$-orthogonal polynomials which are extensions of the Hermite and Laguerre polynomials. The underlying algebraic framework allowed us a systematic derivation of their main properties such as recurrence relations, difference-differential equations, lowering and rising operators and generating functions. Finally, we use these polynomials to construct a realization of the $C_\lambda$-extended oscillator by block matrices.

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Fethi Bouzeffour, Wissem Jedidi. 2019-03-13. $C_\lambda$- Extended oscillator algebra and $d$-orthogonal polynomials. https://arxiv.org/abs/1903.05318

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