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Borel subgroups adapted to nilpotent elements of standard Levi type


Author: Lucas Fresse
Journal: Represent. Theory 18 (2014), 341-360
MSC (2010): Primary 17B08, 20G07, 14M15
DOI: https://doi.org/10.1090/S1088-4165-2014-00458-8
Published electronically: October 27, 2014
Previous version: Original version posted October 27, 2014
Corrected version: Current version corrects changes to the support information.
MathSciNet review: 3272063
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Abstract | References | Similar Articles | Additional Information

Abstract: Let a reductive algebraic group over an algebraically closed field of good characteristic be given. Attached to a nilpotent element of its Lie algebra, we consider a family of algebraic varieties, which incorporates classical objects such as Springer fiber, Spaltenstein varieties, and Hessenberg varieties. When the nilpotent element is of standard Levi type, we show that the varieties of this family admit affine pavings that can be obtained by intersecting with the Schubert cells corresponding to a suitable Borel subgroup.


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Additional Information

Lucas Fresse
Affiliation: Université de Lorraine, CNRS, Institut Élie Cartan de Lorraine, UMR 7502, Vandoeuvre-lès-Nancy, F-54506, France
Email: lucas.fresse@univ-lorraine.fr

DOI: https://doi.org/10.1090/S1088-4165-2014-00458-8
Keywords: Nilpotent orbits, standard Levi type, partial flag varieties, Springer fibers, affine pavings
Received by editor(s): February 10, 2014
Received by editor(s) in revised form: July 15, 2014
Published electronically: October 27, 2014
Additional Notes: This work was supported in part by the ANR project NilpOrbRT (ANR-12-PDOC-0031)
Article copyright: © Copyright 2014 American Mathematical Society

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