关于半单李代数的抛物子代数中的一类双极化

On a Class of Dipolarizations in Parabolic Subalgebras of Semisimple Lie Algebras

本文给出了一种构造复半单李代数抛物子代数中双极化的方法,并给出了其实形式．一般情况下,构造的双极化是非对称的．这种构造方法给出了一大类非可解李代数中极化的例子．后者在表示理论和物理,特别是力学中有重要应用．

This paper gives a method to construct dipolarizations in parabolic subalgebras of complex semisimple Lie algebras as well as some real forms of these Lie algebras. In general, the dipolarizations the author finds are nonsymmetric. This construction presents a large number of polarizations in non-solvable Lie algebras, which has important applications in representation theory and Physics, especially in Mechanics.