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

Orthogonal functions related to Lax pairs in Lie algebras