Mathematics – Representation Theory
Scientific paper
2004-07-21
A shorter version can be found in Journal of Lie Theory 16 (2006), 57-65
Mathematics
Representation Theory
New version contains a new final remark
Scientific paper
In this paper, we study the commuting variety of symmetric pairs associated to parabolic subalgebras with abelian unipotent radical in a simple complex Lie algebra. By using the ``cascade'' construction of Kostant, we construct a Cartan subspace which in turn provides, in certain cases, useful information on the centralizers of non $\mathfrak{p}$-regular semisimple elements. In the case of the rank 2 symmetric pair $(\mathrm{so}_{p+2},\mathrm{so}_{p}\times \mathrm{so}_{2})$, $p\geq 2$, this allows us to apply induction, in view of previous results of the authors, and reduce the problem of the irreducibility of the commuting variety to the consideration of evenness of $\mathfrak{p}$-distinguished elements. Finally, via the correspondence of Kostant-Sekiguchi, we check that in this case, $\mathfrak{p}$-distinguished elements are indeed even, and consequently, the commuting variety is irreducible.
Sabourin Herve
Yu Rupert W. T.
No associations
LandOfFree
On the irreducibility of the commuting variety of a symmetric pair associated to a parabolic subalgebra with abelian unipotent radical does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the irreducibility of the commuting variety of a symmetric pair associated to a parabolic subalgebra with abelian unipotent radical, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the irreducibility of the commuting variety of a symmetric pair associated to a parabolic subalgebra with abelian unipotent radical will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1015