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

摘要

The cohomology H~*(Γ,E) of an arithmetic subgroup Γ of a connected reductive algebraic group G defined over Q 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 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 coefficient system E is regular.