Presents explicit formulas for basic relative invariants and determinants in homogeneous cones, implying significant advancements in invariant theory.
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 .
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H. Nakashima (2014) studied this question.
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