A CHARACTERIZATION OF SYMMETRIC CONES BY THE DEGREES OF BASIC RELATIVE INVARIANTS

Takashi YAMASAKI; Takaaki NOMURA

doi:10.2206/kyushujm.70.237

Kyushu Journal of Mathematics

Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116

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A CHARACTERIZATION OF SYMMETRIC CONES BY THE DEGREES OF BASIC RELATIVE INVARIANTS

Takashi YAMASAKI, Takaaki NOMURA

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Keywords: homogeneous cones, relative invariants, symmetric cones, principal minors, oriented graphs

JOURNAL FREE ACCESS

2016 Volume 70 Issue 2 Pages 237-257

DOI https://doi.org/10.2206/kyushujm.70.237

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Abstract

In this paper, we characterize irreducible symmetric cones among homogeneous cones Ω of rank r by the fact that the basic relative invariants for Ω and for Ω^∗(the dual cone of Ω) both have the degrees 1, 2,... , r, up to permutations.

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