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 \(\mathfrak {sl}(d+1,\mathbb {C})\) is studied in certain representations.

中文翻译：

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李代数中与 Lax 对相关的正交函数

我们在各种表示中研究了 2 参数李代数中的 Lax 对。L的本征函数与标准基的重叠系数以正交多项式和正交函数的形式给出。在某些表示中研究了\(\mathfrak {sl}(d+1,\mathbb {C})\)的 Lax 对的算子L 的特征函数。