Abstract
The cohomology H*(Γ, E) of an arithmetic subgroup Γ of a connected reductive algebraic group G defined over \mathQ can be interpreted in terms of the automorphic spectrum of Γ. In this frame there is a sum decomposition of the cohomology into the cuspidal cohomology ( i.e., classes represented by cuspidal automorphic forms for G) and the so called Eisenstein cohomology. The present paper deals with the case of a quasi split form G of \mathQ-rank two of a unitary group of degree four. We describe in detail the Eisenstein series which give rise to non-trivial cohomology classes and the cuspidal automorphic forms for the Levi components of parabolic \mathQ-subgroups to which these classes are attached. Mainly the generic case will be treated, i.e., we essentially suppose that the coefficient system E is regular.
