E_7和E_8的Weyl群的求和
Summing over the Weyl Groups of E_7 and E_8
摘要：
众所周知，李代数的Weyl群的求和是一个问题，它进入了物理学和数学的许多领域。为此，我们想称之为{ \bf置换权重}的方法以前已经为李代数对$(G_N, A_{N-1})$提出。它现在扩展为$(E_7, A_7)$和$(E_8, A_8)$。显然，这些都是最重要的问题，因此值得单独研究。为了获得这些总结在实践中的结果，它表明，一些简化发生在该方法中，这是以前提出的对$(A_N, A_{N-1})$在一个未发表的工作。
英文摘要：
It is known that summations over Weyl groups of Lie algebras is a problem which enters in many areas of physics as well as in mathematics. For this, a method which we would like to call {\bf permutation weights} has been previously proposed for pairs $(G_N, A_{N-1})$ of Lie algebras. It is now extended for $(E_7, A_7)$ and also $(E_8, A_8)$. It is clear that these are the most non-trivial ones and hence deserve studying separately. In order to obtain the results of these summations in practice, it is shown that some simplifications occur in the method which is previously proposed for pairs $(A_N, A_{N-1})$ in an unpublished work.
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