## Journal of the Mathematical Society of Japan

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

#### Abstract

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 information

Source
J. Math. Soc. Japan, Volume 57, Number 2 (2005), 357-385.

Dates
First available in Project Euclid: 14 September 2006

https://projecteuclid.org/euclid.jmsj/1158242063

Digital Object Identifier
doi:10.2969/jmsj/1158242063

Mathematical Reviews number (MathSciNet)
MR2123237

Zentralblatt MATH identifier
1176.11023

#### Citation

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 57 (2005), no. 2, 357--385. doi:10.2969/jmsj/1158242063. https://projecteuclid.org/euclid.jmsj/1158242063

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