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Computation of Weyl groups of $ G$-varieties


Author: Ivan V. Losev
Journal: Represent. Theory 14 (2010), 9-69
MSC (2010): Primary 14M17, 14R20
DOI: https://doi.org/10.1090/S1088-4165-10-00365-1
Published electronically: January 5, 2010
MathSciNet review: 2577655
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Abstract: Let $ G$ be a connected reductive group. To any irreducible $ G$-variety one assigns a certain linear group generated by reflections called the Weyl group. Weyl groups play an important role in the study of embeddings of homogeneous spaces. We establish algorithms for computing Weyl groups for homogeneous spaces and affine homogeneous vector bundles. For some special classes of $ G$-varieties (affine homogeneous vector bundles of maximal rank, affine homogeneous spaces, homogeneous spaces of maximal rank with a discrete group of central automorphisms) we compute Weyl groups more or less explicitly.


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Additional Information

Ivan V. Losev
Affiliation: Department of Mathematics, Massachusetts Institute of Technology. 77 Massachu- setts Avenue, Cambridge, Massachusetts 02139
Email: ivanlosev@math.mit.edu

DOI: https://doi.org/10.1090/S1088-4165-10-00365-1
Keywords: Reductive groups, homogeneous spaces, Weyl groups, spherical varieties
Received by editor(s): August 7, 2007
Published electronically: January 5, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.