LAUSR

Let Gi be a closed Lie subgroup of U(n), Ωi be a bounded Gi-invariant domain in Cn which contains 0, and $$O{\left( {{\mathbb{C}^n}} \right)^{{G_i}}} = \mathbb{C}$$O(ℂn)Gi=ℂ, for i = 1; 2. If f: Ω1 → Ω2 is a biholomorphism, and f(0) = 0, then f is a polynomial mapping (see Ning et al. (2017)). In this paper, we provide an upper bound for the degree of such polynomial mappings. It is a natural generalization of the well-known Cartan’s theorem.