Rational equivariant holomorphic maps of symmetric domains

Abstract.

An equivariant holomorphic map of symmetric domains associated to a homomorphism of semisimple algebraic groups defined over $\mathbb{Q}$ is rational if it carries a point belonging to a set determined by an arithmetic subgroup to a point in a similar set. We prove that an equivariant holomorphic map of symmetric domains is rational if the associated Kuga fiber variety does not have a nontrivial deformation.