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On Commuting Varieties of Nilradicals of Borel Subalgebras of Reductive Lie Algebras

Part of: Linear algebraic groups and related topics Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  10 October 2014

Simon M. Goodwin  and
Gerhard Röhrle
Simon M. Goodwin
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK, (s.m.goodwin@bham.ac.uk)
Gerhard Röhrle
Affiliation:
Fakultät für MathematikRuhr-Universität Bochum, D-44780 Bochum, Germany, (gerhard.roehrle@rub.de)
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Abstract

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Let G be a connected reductive algebraic group defined over an algebraically closed field of characteristic 0. We consider the commuting variety of the nilradical of the Lie algebra of a Borel subgroup B of G. In case B acts on with only a finite number of orbits, we verify that is equidimensional and that the irreducible components are in correspondence with the distinguishedB-orbits in . We observe that in general is not equidimensional, and determine the irreducible components of in the minimal cases where there are infinitely many B-orbits in .

Keywords

commuting varietiesBorel subalgebrasLie algebrasalgebraic groups

MSC classification

Primary: 20G15: Linear algebraic groups over arbitrary fields
Secondary: 17B45: Lie algebras of linear algebraic groups

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 1 , February 2015 , pp. 169 - 181
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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