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Journal of Lie Theory 11 (2001), No. 1, 155--171
Copyright Heldermann Verlag 2001

Basic Relative Invariants Associated to Homogeneous Cones and Applications

Hideyuki Ishi
Dept. of Mathematical Sciences, Yokohama City University, Yokohama 236-0027, Japan

We determine the basic relative invariants on the ambient vector space of a homogeneous cone Ω under the action of the solvable linear Lie group acting on Ω simply transitively. The results are applied to a study of the Riesz distributions on Ω and to an algebraic description of the closure C(Ω) of Ω.

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