Richardson elements for the classical Lie algebras
Parabolic subalgebras of semi-simple Lie algebras
decompose as $\liea{p}=\liea{m}\oplus\liea{n}$
where $\liea{m}$ is a Levi factor and
$\liea{n}$ the corresponding nilradical.
By Richardsons
theorem \cite{ri},
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
$\liea{gl}_N$ of Br\"ustle, Hille, Ringel and
R\"ohrle \cite{bhrr} 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 \cite{b04}.
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.
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