On the Convexity of the Moment Mapping for Unitary Highest Weight Representations
On the Convexity of the Moment Mapping for Unitary Highest Weight Representations
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关于酉最高权表示的矩映射的凸性
DOI：
10.1006/jfan.1995.1014
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发表时间：
1995
影响因子：
1.7
通讯作者：
K. Neeb
中科院分区：
文献类型：
--
作者：
K. Neeb
对于Hilbert空间H上李群G的每个连续酉表示，我们将光滑向量的射影空间到G的李代数的对偶g* 的矩映射联系起来。对于酉最高权表示，我们得到了该映射的像的闭包是凸的那些最高权的表征，即，等于最高权重轨道的凸船体。这个结果推广了紧群表示和全纯离散级数表示的相应结果。
To each continuous unitary representation of a Lie group G on a Hilbert space H we associate a moment map from the projective space of smooth vectors to the dual g* of the Lie algebra of G. For unitary highest weight representations we obtain a characterization of those highest weights for which the closure of the image of this map is convex, i.e., equal to the convex hull of the highest weight orbit. This result generalizes the corresponding result for representations of compact groups and holomorphic discrete series representations.