Glasnik Matematicki, Vol. 47, No. 2 (2012), 351-372.

THE FRANKE FILTRATION OF THE SPACES OF AUTOMORPHIC FORMS SUPPORTED IN A MAXIMAL PROPER PARABOLIC SUBGROUP

Neven Grbac

Department of Mathematics, University of Rijeka, Radmile Matejčić 2, HR-51000 Rijeka, Croatia
e-mail: neven.grbac@math.uniri.hr

Abstract.   The Franke filtration is a finite filtration of certain spaces of automorphic forms on the adèlic points of a reductive linear algebraic group defined over a number field whose quotients can be described in terms of parabolically induced representations. Decomposing the space of automorphic forms according to their cuspidal support, the Franke filtration can be made more explicit. This paper describes explicitly the Franke filtration of the spaces of automorphic forms supported in a maximal proper parabolic subgroup, that is, in a cuspidal automorphic representation of its Levi factor. Such explicit description is important for applications to computation of automorphic cohomology, and thus the cohomology of congruence subgroups. As examples, the general linear group and split symplectic and special orthogonal groups are treated.

2010 Mathematics Subject Classification.   22E55, 11F70.

Key words and phrases.   Automorphic forms, Franke filtration, Eisenstein series.

Full text (PDF) (free access)

DOI: 10.3336/gm.47.2.10

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