Can one see the signs of structure constants?

N. A. Vavilov

Algebra i analiz, Tome 19 (2007) no. 4, pp. 34-68.

Résumé

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 $\mathrm{E}_l$ .

Détail

Keywords: Microweight representation, adjoint representation, weight diagram, structure constants.

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