The cohomology $H^{*}(\Gamma,E)$ of an arithmetic subgroup $\Gamma$ of a connected reductive algebraic group $G$ defined over $\mathbf{Q}$ can be interpreted in terms of the automorphic spectrum of $\Gamma$ . 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 $\mathbf{Q}$ -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 $\mathbf{Q}$ -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.
@article{1158242063,
author = {HAYATA, Takahiro and SCHWERMER, Joachim},
title = {On arithmetic subgroups of a Q-rank 2 form of SU(2,2) and their automorphic cohomology},
journal = {J. Math. Soc. Japan},
volume = {57},
number = {4},
year = {2005},
pages = { 357-385},
language = {en},
url = {http://dml.mathdoc.fr/item/1158242063}
}
HAYATA, Takahiro; SCHWERMER, Joachim. On arithmetic subgroups of a Q-rank 2 form of SU(2,2) and their automorphic cohomology. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp. 357-385. http://gdmltest.u-ga.fr/item/1158242063/