We apply the theory of \(\phi \)-coordinated modules, developed by H.-S. Li, to the Etingof–Kazhdan quantum affine vertex algebra associated with the trigonometric R-matrix of type A. We prove, for a certain associate \(\phi \) of the one-dimensional additive formal group, that any (irreducible) \(\phi \)-coordinated module for the level \(c\in {\mathbb {C}}\) quantum affine vertex algebra is naturally equipped with a structure of (irreducible) restricted level c module for the quantum affine algebra in type A and vice versa. In the end, we discuss relation between the centers of the quantum affine algebra and the quantum affine vertex algebra.

我们应用了由 H.-S 开发的\(\phi \)协调模块理论。Li，到与A型三角R矩阵相关的 Etingof-Kazhdan 量子仿射顶点代数。我们证明，对于特定副\（\披\）的一维添加剂正规基，任何（不可约）的\（\披\）配位的用于水平模块\（C \在{\ mathbb {C} }\)量子仿射顶点代数自然配备了一个（不可约）限制级c模块的结构，用于A型量子仿射代数反之亦然。最后，我们讨论了量子仿射代数中心与量子仿射顶点代数中心之间的关系。