关于群特征标的计算
On the Calculation of Group Characters
摘要：
众所周知，有限李代数不可约表示的特征标可以用Weyl特征标公式得到，其中包含Weyl群求和，这使得实际计算几乎是不可能的，除了少数低秩李代数。从Weyl特征标公式出发，我们证明了这些特征标可以在不涉及Weyl群求和的情况下重新表示。并以G2李代数为例，详细介绍了一些有用的技术要点。
英文摘要：
It is known that characters of irreducible representations of finite Lie algebras can be obtained using theWeyl character formula including Weyl group summations which make actual calculations almost impossible except for a few Lie algebras of lower rank. By starting from the Weyl character formula, we show that these characters can be re-expressed without referring to Weyl group summations. Some useful technical points are given in detail for the instructive example of G2 Lie algebra.
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