RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zap. Nauchn. Sem. POMI, 2011, Volume 386, Pages 5–99 (Mi znsl3908)  

This article is cited in 5 scientific papers (total in 5 papers)

Chevalley group of type $\mathrm E_7$ in the 56-dimensional representation

N. A. Vavilova, A. Yu. Luzgarevb

a St. Petersburg State University, St. Petersburg, Russia
b Einstein Institute of Mathematics, Hebrew University of Jerusalem

Abstract: The present paper is devoted to a detailed computer study of the action of Chevalley group $G(\mathrm E_7,R)$ on the 56-dimensional minimal module $V(\varpi_7)$. Our main objectives are an explicit choice and tabulation of the signs of structure constants for this action, compatible with a given choice of a positive Chevalley base, construction of multilinear invariants and of the equations, satisfied by the matrix entries of matrices from $G(\mathrm E_7,R)$ in this representation, and explicit tabulation of root elements. These calculations are performed in four numberings of weights: the natural one, as well as those compatible with the $\mathrm A_6$-branching, the $\mathrm D_6$-branching, and the $\mathrm E_6$-branching. Similar tables for the action of Chevalley group $G(\mathrm E_6,R)$ on the 27-dimensional minimal module $V(\varpi_1)$ were published in our joint paper with Igor Pevzner. Bibl. 142 titles.

Key words and phrases: Chevalley groups, exceptional groups, microweight representations, structure constants, invariant forms, root elements.

Full text: PDF file (1016 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2012, 180:3, 197–251

Document Type: Article
UDC: 512.5
Received: 24.11.2010

Citation: N. A. Vavilov, A. Yu. Luzgarev, “Chevalley group of type $\mathrm E_7$ in the 56-dimensional representation”, Problems in the theory of representations of algebras and groups. Part 20, Zap. Nauchn. Sem. POMI, 386, POMI, St. Petersburg, 2011, 5–99; J. Math. Sci. (N. Y.), 180:3 (2012), 197–251

Citation in format AMSBIB
\Bibitem{VavLuz11}
\by N.~A.~Vavilov, A.~Yu.~Luzgarev
\paper Chevalley group of type $\mathrm E_7$ in the 56-dimensional representation
\inbook Problems in the theory of representations of algebras and groups. Part~20
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 386
\pages 5--99
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3908}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 180
\issue 3
\pages 197--251
\crossref{https://doi.org/10.1007/s10958-011-0641-y}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855684282}


Linking options:
  • http://mi.mathnet.ru/eng/znsl3908
  • http://mi.mathnet.ru/eng/znsl/v386/p5

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. A. Vavilov, “Stroenie izotropnykh reduktivnykh grupp”, Tr. In-ta matem., 18:1 (2010), 15–27  mathnet
    2. N. A. Vavilov, “$\mathrm A_3$-dokazatelstvo strukturnykh teorem dlya grupp Shevalle tipov $\mathrm E_6$$\mathrm E_7$. II. Osnovnaya lemma”, Algebra i analiz, 23:6 (2011), 1–31  mathnet  mathscinet  elib; N. A. Vavilov, “An $\mathrm A_3$-proof of the structure theorems for Chevalley groups of types $\mathrm E_6$ and $\mathrm E_7$. II. The main lemma”, St. Petersburg Math. J., 23:6 (2012), 921–942  crossref  isi  elib
    3. N. A. Vavilov, “Decomposition of unipotents for $\mathrm E_6$ and $\mathrm E_7$: 25 years after”, Voprosy teorii predstavlenii algebr i grupp. 27, Zap. nauchn. sem. POMI, 430, POMI, SPb., 2014, 32–52  mathnet  mathscinet
    4. J. Math. Sci. (N. Y.), 209:6 (2015), 922–934  mathnet  crossref
    5. N. A. Vavilov, A. Yu. Luzgarev, “Normalizator gruppy Shevalle tipa $\mathrm E_7$”, Algebra i analiz, 27:6 (2015), 57–88  mathnet  mathscinet  elib; N. A. Vavilov, A. Yu. Luzgarev, “Normaliser of the Chevalley group of type $\mathrm E_7$”, St. Petersburg Math. J., 27:6 (2016), 899–921  crossref  isi
  • Записки научных семинаров ПОМИ
    Number of views:
    This page:286
    Full text:86
    References:9

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2017