Geometry of root elements in groups of type ${\mathrm E}_{6}$
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I. M. Pevzner
Translated by: A. Luzgarev - St. Petersburg Math. J. 23 (2012), 603-635
- DOI: https://doi.org/10.1090/S1061-0022-2012-01210-0
- Published electronically: March 2, 2012
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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.References
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Bibliographic Information
- I. M. Pevzner
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskii Prospekt 28, Petrodvorets, St. Petersburg 198504, Russia
- Email: pevzner_igor@mail.ru
- 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.
- © Copyright 2012 American Mathematical Society
- Journal: St. Petersburg Math. J. 23 (2012), 603-635
- MSC (2010): Primary 17B22
- DOI: https://doi.org/10.1090/S1061-0022-2012-01210-0
- MathSciNet review: 2896171