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arXiv · 1608.05354

An algebraic interpretation of the $q$-Meixner polynomials

Julien Gaboriaud·Luc Vinet
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Abstract

An algebraic interpretation of the $q$-Meixner polynomials is obtained. It is based on representations of $\mathcal{U}_q(\mathfrak{su}(1,1))$ on $q$-oscillator states with the polynomials appearing as matrix elements of unitary $q$-pseudorotation operators. These operators are built from $q$-exponentials of the $\mathcal{U}_q(\mathfrak{su}(1,1))$ generators. The orthogonality, recurrence relation, difference equation, and other properties of the $q$-Mexiner polynomials are systematically obtained in the proposed framework.

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Julien Gaboriaud, Luc Vinet. 2017-04-06. An algebraic interpretation of the $q$-Meixner polynomials. https://doi.org/10.1007/s11139-017-9908-3

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