Year: 2005
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Baur, Karin
Institution: University of California San Diego
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950228804