  We introduce a natural definition of Riesz measures and Wishart laws
associated to an $\Omega$-positive (virtual) quadratic map, where $\Omega
\subset \real^n$ is a regular open convex cone. We give a general formula for
moments of the Wishart laws. Moreover, if the quadratic map has an equivariance
property under the action of a linear group acting on the cone $\Omega$
transitively, then the associated Riesz measure and Wishart law are described
explicitly by making use of theory of relatively invariant distributions on
homogeneous cones.
