Let V be the pseudo-Euclidean vector space of signature (p,q), p>2 and W a
module over the even Clifford algebra Cl^0 (V). A homogeneous quaternionic
manifold (M,Q) is constructed for any spin(V)-equivariant linear map \Pi :
\wedge^2 W \to V. If the skew symmetric vector valued bilinear form \Pi is
nondegenerate then (M,Q) is endowed with a canonical pseudo-Riemannian metric g
such that (M,Q,g) is a homogeneous quaternionic pseudo-K\"ahler manifold.
The construction is shown to have a natural mirror in the category of
supermanifolds. In fact, for any spin(V)-equivariant linear map \Pi : Sym^2 W
\to V a homogeneous quaternionic supermanifold (M,Q) is constructed and,
moreover, a homogeneous quaternionic pseudo-K\"ahler supermanifold (M,Q,g) if
the symmetric vector valued bilinear form \Pi is nondegenerate.Comment: to appear in the Memoirs of the AMS, 81 pages, Latex source fil