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Algebra i Analiz, 2008, Volume 20, Issue 5, Pages 9–40 (Mi aa529)  

This article is cited in 9 scientific papers (total in 9 papers)

Research Papers

Numerology of square equations

N. A. Vavilov

St. Petersburg State University, Department of Mathematics and Mechanics

Keywords: Chevalley groups, polyvector representations, spin representations, minimal modules, highest weight orbit, weight diagram, crystal graph, standard monomial theory, decomposition of unipotents, Plücker equations, Cartan equations, Borel–Freudenthal equations, projective octave plane

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English version:
St. Petersburg Mathematical Journal, 2009, 20:5, 687–707

Bibliographic databases:

MSC: 20G15, 20G35
Received: 01.04.2007

Citation: N. A. Vavilov, “Numerology of square equations”, Algebra i Analiz, 20:5 (2008), 9–40; St. Petersburg Math. J., 20:5 (2009), 687–707

Citation in format AMSBIB
\by N.~A.~Vavilov
\paper Numerology of square equations
\jour Algebra i Analiz
\yr 2008
\vol 20
\issue 5
\pages 9--40
\jour St. Petersburg Math. J.
\yr 2009
\vol 20
\issue 5
\pages 687--707

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    This publication is cited in the following articles:
    1. N. A. Vavilov, S. I. Nikolenko, “$\mathrm A_2$-dokazatelstvo strukturnykh teorem dlya gruppy Shevalle tipa $\mathrm F_4$”, Algebra i analiz, 20:4 (2008), 27–63  mathnet  mathscinet  zmath  elib; N. A. Vavilov, S. I. Nikolenko, “$\mathrm A_2$-proof of structure theorems for Chevalley groups of type $\mathrm F_4$”, St. Petersburg Math. J., 20:4 (2009), 527–551  crossref  isi
    2. N. A. Vavilov, “Some more exceptional numerology”, J. Math. Sci. (N. Y.), 171:3 (2010), 317–321  mathnet  crossref
    3. N. A. Vavilov, “Stroenie izotropnykh reduktivnykh grupp”, Tr. In-ta matem., 18:1 (2010), 15–27  mathnet
    4. N. A. Vavilov, A. Yu. Luzgarev, “Gruppa Shevalle tipa $\mathrm E_7$ v 56-mernom predstavlenii”, Voprosy teorii predstavlenii algebr i grupp. 20, Zap. nauchn. sem. POMI, 386, POMI, SPb., 2011, 5–99  mathnet; N. A. Vavilov, A. Yu. Luzgarev, “Chevalley group of type $\mathrm E_7$ in the 56-dimensional representation”, J. Math. Sci. (N. Y.), 180:3 (2012), 197–251  crossref
    5. 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
    6. 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; J. Math. Sci. (N. Y.), 219:3 (2016), 355–369  crossref
    7. J. Math. Sci. (N. Y.), 209:6 (2015), 922–934  mathnet  crossref
    8. 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
    9. M. M. Atamanova, A. Yu. Luzgarev, “Kubicheskie formy na prisoedinennykh predstavleniyakh isklyuchitelnykh grupp”, Voprosy teorii predstavlenii algebr i grupp. 29, Zap. nauchn. sem. POMI, 443, POMI, SPb., 2016, 9–23  mathnet  mathscinet; M. M. Atamanova, A. Yu. Luzgarev, “Cubic forms on adjoint representations of exceptional groups”, J. Math. Sci. (N. Y.), 222:4 (2017), 370–379  crossref
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