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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)


Can one see the signs of structure constants?

Author: N. A. Vavilov
Translated by: the author
Original publication: Algebra i Analiz, tom 19 (2007), nomer 4.
Journal: St. Petersburg Math. J. 19 (2008), 519-543
MSC (2000): Primary 20G05
Published electronically: May 9, 2008
MathSciNet review: 2381932
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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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Additional Information

N. A. Vavilov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskii Prospekt 28, Staryi Peterhof, St. Petersburg 198504, Russia

PII: S 1061-0022(08)01008-X
Keywords: Microweight representation, adjoint representation, weight diagram, structure constants
Received by editor(s): November 6, 2006
Published electronically: May 9, 2008
Additional Notes: At the final stage of the work, the author was supported by the projects RFBR 03-01-00349 and INTAS 03-51-3251
Article copyright: © Copyright 2008 American Mathematical Society

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