Abstract: Hall has generalized the classical coherent state transform (or Segal-Bargmann transform) on compact Lie Groups and used geometric methods to prove its isometry. The isometry of Bargmann tranform on connected Lie Groups that have compact Lie algebras is proved from the point of view of covering groups.

Key words: Sagel-Bargmann transform, heat kernel, compact Lie algebra

摘要： 从覆盖群的观点证明了具有紧李代数的连通李群上的Bargmann变换的等距同构性。

关键词: Bargmann变换, 热核, 紧李代数