Full paper in PDF:
$% N. Andruskiewitsch’, On the complicatedness of the pair
,
Rev. Mat. Univ. Complut. Madrid 2 (1989), no. 1, 13–28%$.
On the Complicatedness of the Pair
Let
be the complexification of a Cartan decomposition of a
real-semisimple Lie algebra
and let
be the analytic subgroup of the
adjoint group of
with Lie algebra
. Let
be an algebraic connected
linear reductive complex group acting on a finite dimensional vector space
.
In the study of the orbits of this sort of actions, there are some criteria of non
complicatedness e.g., cofreeness (the ring of all polynomial functions on is a free
module over the ring of all L-invariants), etc. From this viewpoint, we show that
the pair is complicated, at least when
is not a product of copies of
or
.
1980 Mathematics Subject Classification (1985 revision): 14D25, 14L30.