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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



An $\mathrm {A}_2$-proof of structure theorems for Chevalley groups of types $\mathrm {E}_6$ and $\mathrm {E}_7$

Authors: N. A. Vavilov and M. R. Gavrilovich
Translated by: N. A. Vavilov
Original publication: Algebra i Analiz, tom 16 (2004), nomer 4.
Journal: St. Petersburg Math. J. 16 (2005), 649-672
MSC (2000): Primary 20G15, 20G35
Published electronically: June 21, 2005
MathSciNet review: 2090851
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N. A. Vavilov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Staryĭ Peterhof, St. Petersburg 198904, Russia

M. R. Gavrilovich
Affiliation: Oxford University, Great Britain

Keywords: Chevalley groups, elementary subgroups, normal subgroups, standard description, minimal module, parabolic subgroups, decomposition of unipotents, root elements, orbit of the highest weight vector, the proof from the Book
Received by editor(s): June 25, 2003
Published electronically: June 21, 2005
Additional Notes: The present paper has been written in the framework of the RFBR projects 01-01-00924 (St. Petersburg State University), 03-01-00349 (POMI RAN). Part of the work was carried out during the authors’ joint stay at the University of Bielefeld supported by SFB-343 and INTAS 00-566. At the final stage, the work was supported by express grants of the Russian Ministry of Higher Education ‘Geometry of root subgroups’ PD02-1.1-371 and ‘Overgroups of semisimple groups’ E02-1.0-61, and the 2003 program of the Presidium of the Russian Academy of Sciences ‘Research in fundamental directions of modern mathematics’.
Article copyright: © Copyright 2005 American Mathematical Society