The Gelfand-Cetlin system and quantization of the complex flag manifolds
The Gelfand-Cetlin system and quantization of the complex flag manifolds
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Gelfand-Cetlin 系统和复旗流形的量化
DOI：
10.1016/0022-1236(83)90092-7
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发表时间：
1983
影响因子：
1.7
通讯作者：
S. Sternberg
中科院分区：
文献类型：
--
作者：
V. Guillemin;S. Sternberg
描述了集体完全可积系统的角作用变量的构造，并确定了相关的Bohr-Sommerfeld集。应用于这类系统的量化方法给出了多重度的公式。对于复标志流形上的Gelfand-Cetlin系统，我们证明了这些公式给出了相关表示的多重性的正确答案。
The construction of angle action variables for collective completely integrable systems is described and the associated Bohr-Sommerfeld sets are determined. The quantization method of Sniatycki applied to such systems gives formulas for multiplicities. For the Gelfand-Cetlin system on complex flag manifolds we show that these formulas give the correct answers for the multiplicities of the associated representations.