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Algebra i Analiz, 2007 Volume 19, Issue 4, Pages 34–68 (Mi aa126)

This article is cited in 33 papers

Research Papers

Can one see the signs of structure constants?

N. A. Vavilov

St. Petersburg State University, Department of Mathematics and Mechanics

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 $\mathrm{E}_l$ .

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

MSC: 20G05

Received: 06.11.2006


 English version:
St. Petersburg Mathematical Journal, 2008, 19:4, 519–543

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