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Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra over$\mathbb{C}$. A $\operatorname{Y}(\mathfrak{g})$-module is said to be weight ifit is a weight $\mathfrak{g}$-module. We give a complete classification ofsimple weight modules for $\operatorname{Y}(\mathfrak{sl}_2)$ which admits aone-dimensional weight space. We prove that there are four classes of suchmodules: finite, highest weight, lowest weight and dense modules. Differentfrom the classical $\mathfrak{sl}_{2}$ representation theory, we show thatthere exist a class of $\operatorname{Y}(\mathfrak{sl}_{2})$ irreduciblemodules which have uniformly 2-dimensional weight spaces.

Simple weight modules for Yangian $\operatorname{Y}(\mathfrak{sl}_{2})$