An invariant-theoretic property of certain CR-mappings

Abstract

Let Γ be a finite group of unitary matrices on ℂ n . For z ∈ ℂ n , the Hermitian symmetric polynomial has been used to construct group-invariant CR-mappings from the sphere to hyperquadrics. We show that the ensuing mappings always contain a complete system of fundamental invariants. This result gives a new algorithm for computing systems of fundamental invariants in invariant rings. A special instance for certain cyclic representations illuminates work by Loehr, Warrington and Wilf who made no mention of invariant theory.