Let
be a quasisimple algebraic group defined over an algebraically closed
field and
a Borel subgroup
of
acting on the
nilradical
of
its Lie algebra
via the adjoint representation. It is known that
has only finitely many orbits in only five cases: when
is type
for
, and when
is type
. We elaborate on this
work in the case when
(type
)
by finding the defining equations of each orbit. We use these equations to determine the
dimension of the orbits and the closure ordering on the set of orbits. The other four cases,
when
is
type
,
can be approached the same way and are treated in a separate paper.
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