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St. Petersburg Mathematical Journal

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Parabolic factorizations of split classical groups


Authors: N. A. Vavilov and S. S. Sinchuk
Translated by: the authors
Original publication: Algebra i Analiz, tom 23 (2011), nomer 4.
Journal: St. Petersburg Math. J. 23 (2012), 637-657
MSC (2010): Primary 20G15, 20G35
DOI: https://doi.org/10.1090/S1061-0022-2012-01211-2
Published electronically: April 13, 2012
MathSciNet review: 2893519
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Abstract | References | Similar Articles | Additional Information

Abstract: An analog of the Dennis-Vaserstein decomposition is proved for an arbitrary pair of maximal parabolic subgroups $ P_r$ and $ P_s$ in split classical groups, under appropriate stability conditions. Before, such decompositions were only known for pairs of terminal parabolic subgroups.


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Additional Information

N. A. Vavilov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskaya ul. 28, Stary Petergof, St. Petersburg 198504, Russia
Email: nikolai-vavilov@yandex.ru

S. S. Sinchuk
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskaya Ul. 28, Stary Petergof, St. Petersburg 198504, Russia
Email: sinchukss@yandex.ru

DOI: https://doi.org/10.1090/S1061-0022-2012-01211-2
Keywords: Split classical groups, elementary subgroup, parabolic subgroups, stability conditions, stable rank, unitary stable rank, Gauss decomposition, Bass–Kolster decomposition, Dennis–Vaserstein decomposition
Received by editor(s): May 21, 2010
Published electronically: April 13, 2012
Additional Notes: The research of the first author was started in the framework of the RFFI project 08-01-00756 “Decompositions of algebraic groups and their applications in representation theory and $K$-theory”. Apart from that, at the final stage his work was supported also by the RFFI projects 09-01-00762, 09-01-00784, 09-01-00878, 09-01-91333, 09-01-90304, and 10-01-90016. The second author acknowledges support of the RFFI project 10-01-92651 “Higher composition laws, algebraic $K$-theory and exceptional groups”.
Dedicated: To Andrei Suslin, with love and admiration
Article copyright: © Copyright 2012 American Mathematical Society

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