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Generation of pairs of short root subgroups in Chevalley groups


Author: V. Nesterov
Translated by: the author
Original publication: Algebra i Analiz, tom 16 (2004), nomer 6.
Journal: St. Petersburg Math. J. 16 (2005), 1051-1077
MSC (2000): Primary 20G15
DOI: https://doi.org/10.1090/S1061-0022-05-00890-3
Published electronically: November 22, 2005
MathSciNet review: 2117453
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Abstract | References | Similar Articles | Additional Information

Abstract: On the basis of the Bruhat decomposition, the subgroups generated by pairs of unipotent short root subgroups in Chevalley groups of type $ \mathrm{B}_{\ell}$, $ \mathrm{C}_{\ell}$, and $ \mathrm{F}_4$ over an arbitrary field are described. Moreover, the orbits of a Chevalley group acting by conjugation on such pairs are classified.


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Additional Information

V. Nesterov
Affiliation: Baltic State Technical University of St. Petersburg, 1st Krasnoarmeiskaya 1, St. Petersburg 190005, Russia
Email: vl.nesterov@mail.ru

DOI: https://doi.org/10.1090/S1061-0022-05-00890-3
Keywords: Chevalley group, unipotent short root subgroups, Bruhat decomposition
Received by editor(s): March 17, 2004
Published electronically: November 22, 2005
Additional Notes: This work was supported by the Ministry of Education of Russia (grants nos. PD02-1.1-371 and E02-1.0-61).
Article copyright: © Copyright 2005 American Mathematical Society

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