A normal form for admissible characters in the sense of Lynch
Parabolic subalgebras $\liea{p}$ of
semisimple Lie algebras
define a $\ZZ$-grading of the Lie algebra.
If there exists a nilpotent element in the
first graded part of $\liea{g}$
on which the adjoint group of
$\liea{p}$ acts with a dense orbit, the parabolic
subalgebra is said to be nice.
The corresponding nilpotent element is also
called admissible.
Nice parabolic subalgebras of simple Lie algebras
have been classified. In the case of Borel subalgebras
a Richardson element of $\liea{g}_1$ is exactly
one that involves all simple root spaces.
It is however difficult to write
down such nilpotent elements for general
parabolic subalgebras. In this paper we give
an explicit construction of admissible
elements in $\liea{g}_1$ that uses as few
root spaces as possible.
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