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On Commuting Varieties of Nilradicals of Borel Subalgebras of Reductive Lie Algebras
Published online by Cambridge University Press: 10 October 2014
Abstract
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
.
MSC classification
- 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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