Torus bundles over locally symmetric varieties associated to cocycles of discrete groups

Abstract

We construct torus bundles over locally symmetric Varieties associated to cocycles in the cohomology group H-2 (Gamma, L), where Gamma 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. 1991 Mathematics Subject Classification: 14G35, 14K99, 11F55.