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St. Petersburg Mathematical Journal

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

 

 

Orthogonal subsets of root systems and the orbit method


Author: M. V. Ignat′ev
Translated by: the author
Original publication: Algebra i Analiz, tom 22 (2010), nomer 5.
Journal: St. Petersburg Math. J. 22 (2011), 777-794
MSC (2010): Primary 17B22
DOI: https://doi.org/10.1090/S1061-0022-2011-01167-7
Published electronically: June 27, 2011
MathSciNet review: 2828828
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Abstract: Let $ k$ be the algebraic closure of a finite field, $ G$ a Chevalley group over $ k$, $ U$ the maximal unipotent subgroup of $ G$. To each orthogonal subset $ D$ of the root system of $ G$ and each set $ \xi$ of $ \vert D\vert$ nonzero scalars in $ k$ one can assign the coadjoint orbit of $ U$. It is proved that the dimension of such an orbit does not depend on $ \xi$. An upper bound for this dimension is also given in terms of the Weyl group.


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Additional Information

M. V. Ignat′ev
Affiliation: Department of Algebra and Geometry, Samara State University, Ak. Pavlova 1, Samara 443011, Russia
Email: mihail.ignatev@gmail.com

DOI: https://doi.org/10.1090/S1061-0022-2011-01167-7
Keywords: Orthogonal subsets of root systems, coadjoint orbits
Received by editor(s): April 14, 2010
Published electronically: June 27, 2011
Article copyright: © Copyright 2011 American Mathematical Society