Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
Basic relative invariants of homogeneous cones and their Laplace transforms
Hideto Nakashima
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2018 Volume 70 Issue 1 Pages 325-344

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Abstract

The purpose of this paper is to show that it is characteristic of symmetric cones among irreducible homogeneous cones that there exists a non-constant relatively invariant polynomial such that its Laplace transform is the reciprocal of a certain polynomial. To prove our theorem, we need the inductive structure of the basic relative invariants of a homogeneous cone. However, we actually work in a more general setting, and consider the inducing of the basic relative invariants from lower rank cones.

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