论文标题
Yangian $ \ operatatorName {y}（\ Mathfrak {sl} _ {2}）$的简单重量模块
Simple weight modules for Yangian $\operatorname{Y}(\mathfrak{sl}_{2})$
论文作者
论文摘要
令$ \ mathfrak {g} $为有限的简单谎言lie代数超过$ \ mathbb {c} $。 $ \ operatorname {y}（\ mathfrak {g}）$ - 如果它是权重$ \ mathfrak {g} $ - module，则说是重量。我们为$ \ operatatorName {y}（\ mathfrak {sl} _2）$提供了简单的重量模块的完整分类，该模块{\ mathfrak {sl} _2）$允许一维重量空间。我们证明有四类此类模块：有限，重量最高，重量最低和密集模块。与经典的$ \ mathfrak {sl} _ {2} $表示理论不同，我们表明存在一类$ \ operatatorName {y}（\ mathfrak {\ mathfrak {sl} _ {2} _ {2}）$不可降低的模块，这些模块具有均匀的2二维重量空间。
Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra over $\mathbb{C}$. A $\operatorname{Y}(\mathfrak{g})$-module is said to be weight if it is a weight $\mathfrak{g}$-module. We give a complete classification of simple weight modules for $\operatorname{Y}(\mathfrak{sl}_2)$ which admits a one-dimensional weight space. We prove that there are four classes of such modules: finite, highest weight, lowest weight and dense modules. Different from the classical $\mathfrak{sl}_{2}$ representation theory, we show that there exist a class of $\operatorname{Y}(\mathfrak{sl}_{2})$ irreducible modules which have uniformly 2-dimensional weight spaces.
