Holomorphic maps of generalized Iwasawa manifolds

Abstract

Let G₁, G₂ be complex Lie groups with$\mathcal{O}(G_1 ) = \mathbb{C}$. Suppose that π: G₁→G₂ is a holomorphic map which takes the identity to the identity. Then π is a homomorphism of groups. In this paper we give an example of the above type of result in the category of homogeneous spaces. In particular we prove that every normalized holomorphic map π: X→Y from a generalized Iwasawa manifold X to a complex manifold Y=G/H, where G is nilpotent and H is discrete, is liftable to a unique group homomorphism. The assumption of discrete isotropy for the range space is essential. Our result follows from a criterion for holomorphic mappings between upper-triangular matrix groups being polynomial.