Special subvarieties in locally symmetric quotients of Mumford-Tate domains

Let X be a quotient of a Mumford-Tate domain D by a discrete subgroup. We define the notion of a special subvariety in X, and formulate a necessary condition for a subvariety to be special, the relative proportionality condition. Finally, we give sufficient criteria for a subvariety of X to be a special subvariety in the sense of the Andre-Oort conjecture.