Conical And Spherical Polynomials

Abstract

Abstract As before, in this chapter V will be a simple Euclidean Jordan algebra, Vℂ its complexification; we will asume that the inner product on Vℂ is given by (z/w) = tr(zw). We will denote by 𝒫 the space of all polynomials on Vℂ. When convenient, we will also think of 𝒫 (without changing notation) as the space of complex-valued polynomials on the real vector space V. A natural representation π of the group GL(Vℂ) is defined on 𝒫 by