Parabolic factorizations of split classical groups
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N. A. Vavilov and S. S. Sinchuk
Translated by: the authors - St. Petersburg Math. J. 23 (2012), 637-657
- DOI: https://doi.org/10.1090/S1061-0022-2012-01211-2
- Published electronically: April 13, 2012
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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.References
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Bibliographic 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
- 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”.
- © Copyright 2012 American Mathematical Society
- 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
- MathSciNet review: 2893519
Dedicated: To Andrei Suslin, with love and admiration