Characterization of the Riesz Exponential Family on homogeneous cones
  In the paper we present a characterization theorem of the Riesz measure and a Wishart exponential family on homogeneous cones through the invariance property of a natural exponential family under the action of the triangular group. 
Hideyuki Ishi and Bartosz Ko{\l}odziejek
math.PR math.ST stat.TH