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arXiv · 2010.06486

Orthogonal functions related to Lax pairs in Lie algebras

Wolter Groenevelt·Erik Koelink
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Abstract

We study a Lax pair in a $2$-parameter Lie algebra in various representations. The overlap coefficients of the eigenfunctions of $L$ and the standard basis are given in terms of orthogonal polynomials and orthogonal functions. Moreover, eigenfunctions for the operator $L$ for a Lax pair for $\mathfrak{sl}(d+1,\mathbb C)$ are studied in certain representations.

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Wolter Groenevelt, Erik Koelink. 2021-03-25. Orthogonal functions related to Lax pairs in Lie algebras. https://arxiv.org/abs/2010.06486

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