Abstract:
The present paper is devoted to a detailed computer study of the action of Chevalley group G(E6,R) on the minimal module V(ϖ1). Our main objectives are an explicit choice and tabulation of the signs of structure constants for this action, compatible with the choice of positive Chevalley base, construction of multilinear invariants and equations on the matrix entries of matrices from G(E6,R) in this representation, and explicit tabulation of root elements.
Citation:
N. A. Vavilov, A. Yu. Luzgarev, I. M. Pevzner, “Chevalley group of type E6 in the 27-dimensional representation”, Problems in the theory of representations of algebras and groups. Part 14, Zap. Nauchn. Sem. POMI, 338, POMI, St. Petersburg, 2006, 5–68; J. Math. Sci. (N. Y.), 145:1 (2007), 4697–4736
\Bibitem{VavLuzPev06}
\by N.~A.~Vavilov, A.~Yu.~Luzgarev, I.~M.~Pevzner
\paper Chevalley group of type $\mathrm E_6$ in the 27-dimensional representation
\inbook Problems in the theory of representations of algebras and groups. Part~14
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 338
\pages 5--68
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl165}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2354606}
\zmath{https://zbmath.org/?q=an:1124.20032}
\elib{https://elibrary.ru/item.asp?id=9305287}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 145
\issue 1
\pages 4697--4736
\crossref{https://doi.org/10.1007/s10958-007-0304-1}
\elib{https://elibrary.ru/item.asp?id=13553073}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34547520972}
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