论文标题
古典谎言代数和国旗品种的多项式表示
Polynomial representations of classical Lie algebras and flag varieties
论文作者
论文摘要
最近，我们启动了一个程序，以描述与多项式矢量场有关的与Dynkin型图相关的LIE代数对通用Verma模块的作用。在本文中，我们解释说，基于整个代数的知识，不仅是简单的根，因此经典ABCD系列的Lie代数系列的结果与更传统的方法相吻合。我们应用coset描述，从大型表示开始，然后在代数的帮助下将其降低，并与原始的代数交通。然后，通过固定该残差对称性来获得不可约的表示。
Recently we have started a program to describe the action of Lie algebras associated with Dynkin-type diagrams on generic Verma modules in terms of polynomial vector fields. In this paper we explain that the results for the classical ABCD series of Lie algebras coincide with the more conventional approach, based on the knowledge of the entire algebra, not only the simple roots. We apply the coset description, starting with a large representation and then reducing it with the help of the algebra, commuting with the original one. The irreducible representations are then obtained by gauge fixing this residual symmetry.
