  Let M_0=G_0/H be a (n+1)-dimensional Cahen-Wallach Lorentzian symmetric space
associated with a symmetric decomposition g_0=h+m and let S(M_0) be the spin
bundle defined by the spin representation r:H->GL_R(S) of the stabilizer H.
This article studies the superizations of M_0, i.e. its extensions to a
homogeneous supermanifold M=G/H whose sheaf of superfunctions is isomorphic to
Lambda(S^*(M_0)). Here G is a Lie supergroup which is the superization of the
Lie group G_0 associated with a certain extension of the Lie algebra g_0 to a
Lie superalgebra g=g_0+g_1=g_0+S, via the Kostant construction. The
construction of the superization g consists of two steps: extending the spin
representation r:h->gl_R(S) to a representation r:g_0->gl_R(S) and constructing
appropriate r(g_0)-equivariant bilinear maps on S. Since the Heisenberg algebra
heis is a codimension one ideal of the Cahen-Wallach Lie algebra g_0, first we
describe spin representations of gheis and then determine their extensions to
g_0. There are two large classes of spin representations of gheis and g_0: the
zero charge and the non-zero charge ones. The description strongly depends on
the dimension n+1 (mod 8). Some general results about superizations g=g_0+g_1
are stated and examples are constructed.
