
Journal of Lie Theory 24 (2014), No. 4, 10131032 Copyright Heldermann Verlag 2014 Basic Relative Invariants of Homogeneous Cones Hideto Nakashima Graduate School of Mathematics, Kyushu University, Fukuoka 8190735, Japan hnakashima@math.kyushuu.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 [ Fulltextpdf (382 KB)] for subscribers only. 