SPECTRUM AND MULTIPLICITIES FOR RESTRICTIONS OF UNITARY REPRESENTATIONS IN NILPOTENT LIE GROUPS
SPECTRUM AND MULTIPLICITIES FOR RESTRICTIONS OF UNITARY REPRESENTATIONS IN NILPOTENT LIE GROUPS
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幂零李群中单一表示的谱和重数限制
DOI：
10.2140/pjm.1988.135.233
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发表时间：
1988
影响因子：
0.6
通讯作者：
F. Greenleaf
中科院分区：
文献类型：
--
作者：
L. Corwin;F. Greenleaf
设G是连通的单连通幂零李群，AT是李群。我们考虑以下问题：对于<G G A，如何将U\K分解为直接积分？在他的开创性论文陈述幂零李群，基里洛夫了定性的描述;我们的答案在这里给出了多重性的陈述出现在直接积分，但几何的性质和非常精神的基里洛夫轨道图片。
Let G be a connected, simply connected nilpotent Lie group, and let AT be a Lie subgroup. We consider the following question: for <G G A, how d° es one decompose U\K as a direct integral? In his pioneering paper on representations of nilpotent Lie groups, Kirillov gave a qualitative description; our answer here gives the multiplicities of the representations appearing in the direct integral, but is geometric in nature and very much in the spirit of the Kirillov orbit picture.