Torus Bundles over Locally Symmetric Varieties Associated to Cocycles of Discrete Groups

 We construct torus bundles over locally symmetric varieties associated to cocycles in the cohomology group , where Γ is a discrete subgroup of a semisimple Lie group and L is a lattice in a real vector space. We prove that such a torus bundle has a canonical complex structure and that the space of holomorphic forms of the highest degree on a fiber product of such bundles is isomorphic to the space of mixed automorphic forms of a certain type. (Received 4 September 1998)