Abstract:In this article, we define an algebraic version of the Knizhnik–Zamolodchikov (KZ) functor for the degenerate double affine Hecke algebras (a.k.a. trigonometric Cherednik algebras). We compare it with the KZ monodromy functor constructed by Varagnolo–Vasserot. We prove the double centraliser property for our functor and give a characterisation of its kernel. We establish these results for a family of algebras, called quiver double Hecke algebras, which includes the degenerate double affine Hecke algebras as special cases.

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中文翻译：

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简并双仿射 Hecke 代数的 Knizhnik–Zamolodchikov 函子：代数理论

摘要：在本文中，我们为退化双仿射 Hecke 代数（又名三角 Cherednik 代数）定义了 Knizhnik-Zamolodchikov (KZ) 函子的代数版本。我们将其与由 Varagnolo-Vasserot 构建的 KZ 单调函子进行比较。我们证明了我们的函子的双中心属性，并给出了它的内核的特征。我们为一个称为 quiver 双 Hecke 代数的代数族建立了这些结果，其中包括作为特例的退化双仿射 Hecke 代数。

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