  Bobecka and Wesolowski (2002) have shown that, in the Olkin and Rubin
characterization of the Wishart distribution (See Casalis and Letac (1996)),
when we use the division algorithm defined by the quadratic representation and
replace the property of invariance by the existence of twice differentiable
densities, we still have a characterization of the Wishart distribution. In the
present work, we show that, when we use the division algorithm defined by the
Cholesky decomposition, we get a characterization of the Riesz distribution.
