Summing over the Weyl Groups of E_7 and E_8

Details Summing over the Weyl Groups of E_7 and E_8 Summing over the Weyl Groups of E_7 and E_8

1998-12-17

arxiv.org/abs/math-ph/9812014v1

Physics

Mathematical Physics

14 pages, TeX format

Scientific paper

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it is shown that some simplifications occur in the method which is previously proposed for pairs $(A_N, A_{N-1})$ in an unpublished work.

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