Original scientific paper

https://doi.org/10.3336/gm.47.2.10

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

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.

Keywords

Automorphic forms; Franke filtration; Eisenstein series

Hrčak ID:

93949

URI

https://hrcak.srce.hr/93949

Publication date:

19.12.2012.

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