Journal of Lie Theory 24 (2014), No. 4, 1013--1032
Copyright Heldermann Verlag 2014
Basic Relative Invariants of Homogeneous Cones
Hideto Nakashima
Graduate School of Mathematics, Kyushu University, Fukuoka 819-0735, Japan
h-nakashima@math.kyushu-u.ac.jp
The purpose of this paper is to give an explicit expression to the basic relative invariants of a homogeneous cone in terms of the polynomials introduced by Vinberg in 1963. We present a closed formula that exhibits how we obtain the basic relative invariants at one time. We also factorize the determinant of the right multiplication operators of the corresponding clan V by giving an explicit expression to the exponents of the basic relative invariants in terms of the data of V.
Keywords: Basic relative invariants, homogeneous cones, clans.
MSC: 17D99; 43A85, 22E25, 11S90
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