关于李代数及其表示的玻色子实现和非齐性微分实现

ON BOSON REALIZATIONS AND INHOMOGENEOUS DIFFERENTIAL REALIZATION FOR LIE ALGEBRAS AND THEIR REPRESENTATIONS

本文分析和推广了作者以前建议的构造李代数不可分解表示的玻色子实现方法。不仅证明该方法构造的主表示可以在子空间上导出Gruber的主表示,而且讨论了该表示的商空间表示与相干态的联系.本文还建议了构造李代数非齐性玻色子实现的一般方法,由此得到了量子力学准精确可解问题中有用的李代数非齐性微分实现。

In this paper we systematically analyse and generalize the Boson Realization Method proposed by the author for constructing indecomposable representations of Lie (super) algebras. We prove that the representations thus obtained cover the master representation of Gruber and point out the relation of its coset representation to the boson coherent states. We also propose a general method of finding the inhomogeneous differential realizations of lie algebras from their indecomposable representations, which is very useful in new found quantum mechanical quasiexactly solvable problems.