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A. The cohomology H ⁄ (¡, E) of an arithmetic subgroup ¡ of a connected reductive algebraic group G de£ned over Q can be interpreted in terms of the automorphic spectrum of ¡. In this frame there is a sum decomposition of the cohomology into the cuspidal co-homology (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 Q-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 Q-subgroups to which these classes are attached. Mainly the generic case will be treated, i.e., we essentially suppose that the coe–cient system E is regular.

On arithmetic subgroups of a Q-rank 2 form of SU(2,2) and their automorphic cohomology