Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

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

Request Permissions   Purchase Content 


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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 17B22

Retrieve articles in all journals with MSC (2010): 17B22

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}

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