Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 57, Number 2 (2005), 357-385.
On arithmetic subgroups of a Q-rank 2 form of SU(2,2) and their automorphic cohomology
The cohomology of an arithmetic subgroup of a connected reductive algebraic group defined over can be interpreted in terms of the automorphic spectrum of . In this frame there is a sum decomposition of the cohomology into the cuspidal cohomology ( i.e., classes represented by cuspidal automorphic forms for ) and the so called Eisenstein cohomology. The present paper deals with the case of a quasi split form of -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 -subgroups to which these classes are attached. Mainly the generic case will be treated, i.e., we essentially suppose that the coefficient system is regular.
J. Math. Soc. Japan, Volume 57, Number 2 (2005), 357-385.
First available in Project Euclid: 14 September 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11F75: Cohomology of arithmetic groups
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
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