A SHORTER PROOF OF A CHARACTERIZATION OF SYMMETRIC CONES BY THE DEGREES OF THE BASIC RELATIVE INVARIANTS
2017 Volume 71 Issue 2 Pages 251-255
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2017 Volume 71 Issue 2 Pages 251-255
The aim of this paper is to give a shorter proof to the main theorem of Yamasaki-Nomura in 2016, stating that a homogeneous cone of rank r is an irreducible symmetric cone if and only if the basic relative invariants of the cone and of the dual cone both have the degrees 1, 2,... ,r, up to permutations. Our proof is based on the multiplier matrix of homogeneous cones studied in detail by the present author.
