  In this paper we treat faithful actions of simple algebraic groups on
irreducible modules and on the associated Grassmannian varieties. By explicit
calculation, we show that in each case, with essentially one exception, there
is a dense open subset any point of which has stabilizer conjugate to a fixed
subgroup, called the generic stabilizer. We provide tables listing generic
stabilizers in the cases where they are non-trivial; in addition we decide
whether or not there is a dense orbit, or a regular orbit for the action on the
module.
