In this paper we first construct an analytic realization of the C_λ-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_λ-extended oscillator by block matrices.

中文翻译：

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Cλ-扩展的振荡器代数和d-正交多项式

在本文中，我们首先构建一个分析实现的Ç _λ -Extended振荡器代数差微分算子的帮助。其次，我们研究d正交多项式的族，这是Hermite和Laguerre多项式的扩展。潜在的代数框架使我们能够系统地推导其主要性质，例如递归关系，差分-微分方程，运算符的下降和上升以及生成函数。最后，我们使用这些多项式来构造实现的Ç _λ由块矩阵-Extended振荡器。