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New models for the action of Hecke operators in spaces of Maass wave forms

Ian Kiming (2007)

Annales de l’institut Fourier

Utilizing the theory of the Poisson transform, we develop some new concrete models for the Hecke theory in a space M λ ( N ) of Maass forms with eigenvalue 1 / 4 - λ 2 on a congruence subgroup Γ 1 ( N ) . We introduce the field F λ = ( λ , n , n λ / 2 n ) so that F λ consists entirely of algebraic numbers if λ = 0 .The main result of the paper is the following. For a packet Φ = ( ν p p N ) of Hecke eigenvalues occurring in M λ ( N ) we then have that either every ν p is algebraic over F λ , or else Φ will – for some m – occur in the first cohomology of a certain space W λ , m which is a...

Non-abelian extensions of infinite-dimensional Lie groups

Karl-Hermann Neeb (2007)

Annales de l’institut Fourier

In this article we study non-abelian extensions of a Lie group G modeled on a locally convex space by a Lie group N . The equivalence classes of such extension are grouped into those corresponding to a class of so-called smooth outer actions S of G on N . If S is given, we show that the corresponding set Ext ( G , N ) S of extension classes is a principal homogeneous space of the locally smooth cohomology group H s s 2 ( G , Z ( N ) ) S . To each S a locally smooth obstruction class χ ( S ) in a suitably defined cohomology group H s s 3 ( G , Z ( N ) ) S is defined....

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