论文标题
schr {Ö} dinger lie代数$（n+1）$ dimensional时空时
Irreducible weight modules over the Schr{ö}dinger Lie algebra in $(n+1)$ dimensional space-time
论文作者
论文摘要
在本文中，我们研究了schr {Ö} dinger lie代数$ \ mathfrak {s} _n $的权重表示。事实证明，多项式差分运算符可以实现代数$ \ mathfrak {s} _n $。使用此实现，我们将对任何$ n $的有限维度重量空间提供了不可约权重$ \ mathfrak {s} _n $模块的完整分类。所有此类模块都可以清楚地表征$ \ Mathfrak {so} _n $ -Modules，$ \ Mathfrak {Sl} _2 $ -Modules和模块上的张量产品。
In this paper, we study weight representations over the Schr{ö}dinger Lie algebra $\mathfrak{s}_n$ for any positive integer $n$. It turns out that the algebra $\mathfrak{s}_n$ can be realized by polynomial differential operators. Using this realization, we give a complete classification of irreducible weight $\mathfrak{s}_n$-modules with finite dimensional weight spaces for any $n$. All such modules can be clearly characterized by the tensor product of $\mathfrak{so}_n$-modules, $\mathfrak{sl}_2$-modules and modules over the Weyl algebra.
