  We find a necessary condition for the existence of an action of a Lie group
$G$ by quaternionic automorphisms on an integrable quaternionic manifold in
terms of representations of $\mathfrak{g}$. We check this condition and prove
that a Riemannian symmetric space of dimension $4n$ for $n\geq 2$ has an
invariant integrable almost quaternionic structure if and only if it is
quaternionic vector space, quaternionic hyperbolic space or quaternionic
projective space.
