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 .
H. Nakashima (Wed,) studied this question.
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