St. Petersburg Mathematical Journal

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ISSN 1547-7371(e) ISSN 1061-0022(p)

Can one see the signs of structure constants?

Author(s): 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
Posted: May 9, 2008
MathSciNet review: 2381932
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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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