Abstract

Let X be an irreducible Hermitian symmetric space of noncompact type and rank r. Let p in X and let K be the isotropy group of p in the group of biholomorphic transformations. Let S denote the symmetric algebra in the holomorphic tangent space to X at p. Then S is multiplicity free as a representation of K and the irreducible constituents are parametrized by r-tuples, (m₁,…,m_r) with m₁ ≥… ≥ m_r ≥ 0. That is, the same parameters as the irreducible polynomial representations of GL(r). Let S[m₁,…,m_r] be the corresponding isotypic component. In this article we show that the product in S, S[m₁,…,m_r]S[k,0,0,…,0] is a direct sum of constituents following precisely the classical Pieri rule.

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