Jacobi群的Plancherel定理与群代数的左理想
Plancherel Theorem and the Left Ideals of the Group Algebra for the Jacobi Group
摘要：
设G是三维连通实半单李群，KAN是G的Iwasawa分解，J是Jacobi群，它是两个群Heisenberg群与G的半直积.雅可比群在量子力学中起着重要的作用。本文定义了傅里叶变换，从而得到了群J的Plancherel定理，并由此对Jacobi群的群代数的所有左理想进行了分类
英文摘要：
Let G be the three dimensional connected real semisimple Lie group and let KAN be the Iwasawa decomposition of G.Let J be the Jacobi group, which is the semidirect product of the two groups Heisenberg group with G. The Jacobi group plays an important role in Quantum Mechanics. The purpose of this paper is to define the Fourier transform in order to obtain the Plancherel theorem for the group J. To this end a classification of all left ideals of the group algebra for the Jacobi group
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