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arXiv · 2309.03916

Differential Operator Representation of sl (2, R) as Modules over Univariate and Bivariate Hermite Polynomials

Manouchehr Amiri
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Abstract

This paper presents the connections between univariate and bivariate Hermite polynomials and associated differential equations with specific representations of Lie algebra sl(2,R) whose Cartan sub-algebras coincide the associated differential operators of these differential equations . Applying the Baker-Campbell-Hausdorff formula to generators of these algebras, results in new relation for one-variable and Bivariate Hermite polynomials. A general form of sl(2,R) representation by differential operators and arbitrary polynomial basis such as Laguerre and Legendre polynomials is introduced.

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BibTeXRIS

Manouchehr Amiri. 2023-09-04. Differential Operator Representation of sl (2, R) as Modules over Univariate and Bivariate Hermite Polynomials. https://arxiv.org/abs/2309.03916

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