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April, 2005 On arithmetic subgroups of a Q-rank 2 form of SU(2,2) and their automorphic cohomology
Takahiro HAYATA, Joachim SCHWERMER
J. Math. Soc. Japan 57(2): 357-385 (April, 2005). DOI: 10.2969/jmsj/1158242063


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.


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Takahiro HAYATA. Joachim SCHWERMER. "On arithmetic subgroups of a Q-rank 2 form of SU(2,2) and their automorphic cohomology." J. Math. Soc. Japan 57 (2) 357 - 385, April, 2005.


Published: April, 2005
First available in Project Euclid: 14 September 2006

zbMATH: 1176.11023
MathSciNet: MR2123237
Digital Object Identifier: 10.2969/jmsj/1158242063

Primary: 11F75
Secondary: 11F70 , 22E40

Keywords: associate parabolic subgroup , automorphic representation , cohomology of arithmetic subgroups , cuspidal cohomology , Eisenstein cohomology , minimal coset representatives

Rights: Copyright © 2005 Mathematical Society of Japan


Vol.57 • No. 2 • April, 2005
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