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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 338, Pages 5–68 (Mi znsl165)  
This article is cited in 27 scientific papers (total in 27 papers)

Chevalley group of type $\mathrm E_6$ in the 27-dimensional representation

N. A. Vavilov, A. Yu. Luzgarev, I. M. Pevzner

Saint-Petersburg State University
Full-text PDF (540 kB) Citations (27)
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Abstract: The present paper is devoted to a detailed computer study of the action of Chevalley group $G(\mathrm E_6,R)$ on the minimal module $V(\varpi_1)$. 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 $G(\mathrm E_6,R)$ in this representation, and explicit tabulation of root elements.
Received: 09.11.2006
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 145, Issue 1, Pages 4697–4736
DOI: https://doi.org/10.1007/s10958-007-0304-1
Bibliographic databases:
UDC: 512.5
Language: Russian
Citation: N. A. Vavilov, A. Yu. Luzgarev, I. M. Pevzner, “Chevalley group of type $\mathrm E_6$ 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
Citation in format AMSBIB
\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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    • This publication is cited in the following 27 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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