论文标题
谎言超级甲壳虫的广义Casimir操作员
Generalized Casimir Operators for Lie Superalgebras
论文作者
论文摘要
在本文中，我们将广义的Casimir操作员定义为循环竞争者的超级甲壳虫，并证明他们与基础的谎言超级甲壳虫通勤。这些操作员在张量产品模块的分解中具有应用。我们进一步介绍了通用的Gelfand不变性的概念，用于循环通用线性谎言，并表明它们也与底层谎言超级级别的superalgebra上下班。这些操作员在张量产品模块中应用于最高权重矢量时，这些操作员再次诱导新的最高权重矢量。
In this paper, we define generalized Casimir operators for a loop contragredient Lie superalgebra and prove that they commute with the underlying Lie superalgebra. These operators have applications in the decomposition of tensor product modules. We further introduce the notion of generalized Gelfand invariants for the loop general linear Lie superalgebra and show that they also commute with the underlying Lie superalgebra. These operators when applied to a highest weight vector in a tensor product module again induces a new highest weight vector.
