A FORMULA FOR THE MULTIPLICITY OF A WEIGHT.
A FORMULA FOR THE MULTIPLICITY OF A WEIGHT.
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DOI：
10.1073/pnas.44.6.588
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发表时间：
1958-06
影响因子：
11.1
通讯作者：
B. Kostant
中科院分区：
文献类型：
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作者：
B. Kostant
设g是复半单李代数，h是g的Cartan子代数。是有限维向量空间V？上g的最高权？的不可约表示。E.Cartan的一个著名定理断言，？的最高重量？以重数一的形式发生。更广泛地说，确定任意权重的重数是一个由来已久的问题。Weyl公式(1.12)表示？？H上的函数？？(？)=tr exp？？(？)，？？h的表达式是？以及与表示法无关的量。
Let g be a complex semi-simple Lie algebra and h a Cartan subalgebra of g. Let ?? be an irreducible representation of g, with highest weight ?, on a finite dimensional vector space V ?. A well known theorem of E. Cartan asserts that the highest weight, ?, of ?? occurs with multiplicity one. It has been a question of long standing to determine, more generally, the multiplicity of an arbitrary weight of ??. Weyl’s formula (1.12) for the character of ?? is an expression for the function ??(?) = tr exp ??(?), ??h, on h in terms of ? and quantities independent of the representation.