Journal of Lie Theory, Vol. 11, No. 1, pp. 155-171 (2001)

Basic relative invariants associated to homogeneous cones and applications

Hideyuki Ishi

Department of Mathematical Sciences
Yokohama City University
Yokohama 236-0027

Abstract: In this paper, we determine the basic relative invariants on the ambient vector space of a homogeneous cone $\Omega$ under the action of the solvable linear Lie group acting on $\Omega$ simply transitively. The results are applied to a study of the Riesz distributions on $\Omega$ and to an algebraic description of the closure $\overline{\Omega}$ of $\Omega$.

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