CASIMIR OPERATORS FOR SEMISIMPLE LIE GROUPS
CASIMIR OPERATORS FOR SEMISIMPLE LIE GROUPS
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半单李群的卡西米尔算子
DOI：
10.1070/im1968v002n06abeh000731
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发表时间：
1968
期刊：
影响因子：
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通讯作者：
V. Popov
中科院分区：
文献类型：
--
作者：
A. Perelomov;V. Popov
给出了一种计算半单李群中任意阶p的不变算子（Casimir算子）的特征值的简单方法.所得公式（52）和（55）适用于给定群的不可约表示中至少有一个表示具有单谱的情况-特别是对于所有经典群以及群G2、E6和E7。在经典群的情况下，找到了Casimir算子的生成函数的表达式（见（75））。
A simple method is developed for computing the eigenvalues of the invariant operators (the so-called Casimir operators) Ĉp of arbitrary order p for semisimple Lie groups. The resulting formulas (52) and (55) are applicable for the case that among the irreducible representations of the given group there is at least one representation with a simple spectrum — in particular, for all the classical groups, as well as the groups G2, E6, and E7. An expression is found (see (75)) for the generating function of the Casimir operators in the case of the classical groups.