Abstract
Abstract
Let
${\mathfrak g}$
be a complex simple Lie algebra and
${\mathfrak n}$
the nilradical of a parabolic subalgebra of
${\mathfrak g}$
. We consider some properties of the coadjoint representation of
${\mathfrak n}$
and related algebras of invariants. This includes (i) the problem of existence of generic stabilizers, (ii) a description of the Frobenius semiradical of
${\mathfrak n}$
and the Poisson center of the symmetric algebra , (iii) the structure of as -module, and (iv) the description of square integrable (= quasi-reductive) nilradicals. Our main technical tools are the Kostant cascade in the set of positive roots of
${\mathfrak g}$
and the notion of optimization of
${\mathfrak n}$
.
Publisher
Canadian Mathematical Society