Mathematics – Representation Theory
Scientific paper
2005-01-21
Journal of Algebra (2006), Vol 297/1, 168-185
Mathematics
Representation Theory
16 pages
Scientific paper
Parabolic subalgebras of semi-simple Lie algebras decompose as $\frak{p}=\frak{m}\oplus\frak{n}$ where $\frak{m}$ is a Levi factor and $\frak{n}$ the corresponding nilradical. By Richardsons theorem, there exists an open orbit under the action of the adjoint group $P$ on the nilradical. The elements of this dense orbits are known as Richardson elements. In this paper we describe a normal form for Richardson elements in the classical case. This generalizes a construction for the general linear group of Bruestle, Hille, Ringel and Roehrle to the other classical Lie algebra and it extends the authors normal forms of Richardson elements for nice parabolic subalgebras of simple Lie algebras to arbitrary parabolic subalgebras of the classical Lie algebras. As applications we obtain a description of the support of Richardson elements and we recover the Bala-Carter label of the orbit of Richardson elements.
No associations
LandOfFree
Richardson elements for classical Lie algebras 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 Richardson elements for classical Lie algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Richardson elements for classical Lie algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-593897