We consider generalizations of the BC -type relativistic Calogero–Moser–Sutherland models, comprising of the rational, trigonometric, hyperbolic, and elliptic cases, due to Koornwinder and van Diejen, and construct an explicit eigenfunction for these generalizations. In special cases, we find the various kernel function identities, and also a Chalykh–Feigin–Sergeev–Veselov type deformation of these operators and their corresponding kernel functions, which generalize the known kernel functions for the Koornwinder–van Diejen models.

中文翻译：

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变形 Koornwinder-van Diejen 模型的源标识和核函数

由于 Koornwinder 和 van Diejen，我们考虑了 BC 型相对论 Calogero-Moser-Sutherland 模型的推广，包括有理、三角、双曲线和椭圆情况，并为这些推广构建一个明确的特征函数。在特殊情况下，我们发现了各种核函数恒等式，以及这些算子及其相应核函数的 Chalykh-Feigin-Sergeev-Veselov 型变形，它们概括了 Koornwinder-van Diejen 模型的已知核函数。