Can one see the signs of structure constants?

Vavilov, N.

doi:10.1090/S1061-0022-08-01008-X

Can one see the signs of structure constants?
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by N. A. Vavilov
Translated by: the author

St. Petersburg Math. J. 19 (2008), 519-543

DOI: https://doi.org/10.1090/S1061-0022-08-01008-X

Published electronically: May 9, 2008

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Abstract:

It is described how one can see the signs of action structure constants directly in the weight diagram of microweight and adjoint representations for groups of types $\mathrm {E}_6$, $\mathrm {E}_7$, and $\mathrm {E}_8$. This generalizes the results of the preceding paper, “A third look at weight diagrams”, where a similar algorithm was discussed for microweight representations of $\mathrm {E}_6$ and $\mathrm {E}_7$. The proofs are purely combinatorial and can be viewed as an elementary construction of Lie algebras and Chevalley groups of types $\mathrm {E}_l$.

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