In this paper we define and study a critical-level generalization of the Suzuki functor, relating the affine general linear Lie algebra to the rational Cherednik algebra of type A. Our main result states that this functor induces a surjective algebra homomorphism from the centre of the completed universal enveloping algebra at the critical level to the centre of the rational Cherednik algebra at t = 0. We use this homomorphism to obtain several results about the functor. We compute it on Verma modules, Weyl modules, and their restricted versions. We describe the maps between endomorphism rings induced by the functor and deduce that every simple module over the rational Cherednik algebra lies in its image. Our homomorphism between the two centres gives rise to a closed embedding of the Calogero–Moser space into the space of opers on the punctured disc. We give a partial geometric description of this embedding.

在本文中，我们定义和研究了Suzuki函子的临界级泛化，将仿射一般线性Lie代数与A型有理Cherednik代数相关。在t处完成了有理Cherednik代数中心的临界级的通用包络代数=0。我们使用这种同态性来获得有关函子的多个结果。我们在Verma模块，Weyl模块及其受限版本上进行计算。我们描述了由函子引起的同构环之间的映射，并推断出有理Cherednik代数上的每个简单模块都位于其图像中。我们在两个中心之间的同态性导致Calogero-Moser空间封闭地插入穿孔盘上的手术室。我们对此嵌入进行了部分几何描述。