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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

   

 

Geometry of root elements in groups of type $ {\mathrm E}_{6}$


Author: I. M. Pevzner
Translated by: A. Luzgarev
Original publication: Algebra i Analiz, tom 23 (2011), nomer 3.
Journal: St. Petersburg Math. J. 23 (2012), 603-635
MSC (2010): Primary 17B22
Published electronically: March 2, 2012
MathSciNet review: 2896171
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Abstract: Root elements in the 27-dimensional representation of the simply connected Chevalley group of type $ \mathrm E_7$ over a field are studied. With every root subgroup, a certain six-dimensional singular subspace is associated; this correspondence is shown to be a natural bijection. Also, the notion of the angle between root subgroups is described in terms of singular subspaces.


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Additional Information

I. M. Pevzner
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskii Prospekt 28, Petrodvorets, St. Petersburg 198504, Russia
Email: pevzner{\textunderscore}igor@mail.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2012-01210-0
Keywords: Chevalley groups, exceptional groups, root elements, singular subspaces
Received by editor(s): June 21, 2010
Published electronically: March 2, 2012
Additional Notes: Supported by the joint project of DAAD and the Russian Ministry of Higher Education “Mikhail Lomonosov”, and by the RFBR project 09-01-00784-a.
Article copyright: © Copyright 2012 American Mathematical Society



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