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This article is cited in 32 scientific papers (total in 32 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.
Received: 06.11.2006
Citation:
N. A. Vavilov, “Can one see the signs of structure constants?”, Algebra i Analiz, 19:4 (2007), 34–68; St. Petersburg Math. J., 19:4 (2008), 519–543
Linking options:
https://www.mathnet.ru/eng/aa126 https://www.mathnet.ru/eng/aa/v19/i4/p34
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