Commuting difference operators with polynomial eigenfunctions
Commuting difference operators with polynomial eigenfunctions
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发表时间：
1993-06
影响因子：
1.8
通讯作者：
J. F. van Diejen
中科院分区：
文献类型：
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作者：
J. F. van Diejen
我们提出了一个代数的交换差分算子与三角系数的显式生成元。算子同时对角化最近发现的q-多项式（即Koornwinder的多变量推广的Askey-Wilson多项式）。从物理学的观点来看，这个代数可以解释为由一个新的差分型可积系统的量子积分组成。该系统推广了与非例外根系相关的Calogero-Moser系统。
We present explicit generators of an algebra of commuting difference operators with trigonometric coefficients. The operators are simultaneously diagonalized by recently discovered q-polynomials (viz. Koornwinder's multivariable generalization of the Askey-Wilson polynomials). From the viewpoint of physics the algebra can be interpreted as consisting of the quantum integrals of a novel difference-type integrable sytem. This system generalizes the Calogero-Moser systems associated with non-exceptional root systems.