Adelic Maass spaces on U(2,2)

2007/06/19 by Krzysztof Klosin, Klosin, Krzysztof
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.0706.2828

Abstract

Generalizing the results of Kojima, Gritsenko and Krieg, we define an adelic version of the Maass space for hermitian modular forms of weight k regarded as functions on adelic points of the quasi-split unitary group U(2,2) associated with an imaginary quadratic extension F/Q of discriminant D_F. When the class number h_F of F is odd, we show that the Maass space is invariant under the action of the local Hecke algebras of U(2,2)(Q_p) for all p not dividing D_F. As a consequence we obtain a Hecke-equivariant injective map from the Maass space to the h_F-fold direct product of the space of elliptic modular forms of weight k-1 and level D_F.

Citations

• On the Saito-Kurokawa lifting

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