Orthogonal functions related to Lax pairs in Lie algebras

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. Eigenfunctions for the operator L for a Lax pair for sl(d+ 1 , C) is studied in certain representations.Analysi