Orthogonal functions related to Lax pairs in Lie algebras

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.

arXiv comment26 pages, to appear in Ramanujan J (special issue dedicated to Richard Askey)