In this paper, we study the weighted composition operator on the Fock space $\mf$ of slice regular functions. First, we characterize the boundedness and compactness of the weighted composition operator. Subsequently, we describe all the isometric composition operators. Finally, we introduce a kind of (right)-anti-complex-linear weighted composition operator on $\mf$ and obtain some concrete forms such that this (right)-anti-linear weighted composition operator is a (right)-conjugation. Specially, we present equivalent conditions ensuring weighted composition operators which are conjugate $\mathcal{C}_{a,b,c}-$commuting or complex $\mathcal{C}_{a,b,c}-$ symmetric on $\mf$, which generalized the classical results on $\mathcal{F}^2(\mathbb{C}).$ At last part of the paper, we exhibit the closed expression for the kernel function of $\mf.$

中文翻译：

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四元数 Fock 空间上的加权合成算子

在本文中，我们研究了切片正则函数的 Fock 空间 $\mf$ 上的加权组合算子。首先，我们描述了加权组合算子的有界性和紧凑性。随后，我们描述了所有等距合成算子。最后，我们在 $\mf$ 上引入了一种（右）-反复线性加权组合算子，并获得了一些具体形式，使得该（右）-反线性加权组合算子是一个（右）-共轭。特别地，我们提出了等价条件，确保加权复合算子是共轭 $\mathcal{C}_{a,b,c}-$commuting 或复数 $\mathcal{C}_{a,b,c}-$ 对称于$\mf$，概括了 $\mathcal{F}^2(\mathbb{C}) 上的经典结果。$ 在论文的最后一部分，我们展示了 $\mf.$ 核函数的封闭表达式