On the lifting of elliptic cusp forms to cusp forms on quaternionic unitary groups |
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Authors: | Shunsuke Yamana |
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Institution: | Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan |
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Abstract: | Let H be a definite quaternion algebra over Q with discriminant DH and R a maximal order of H. We denote by Gn a quaternionic unitary group and put Γn=Gn(Q)∩GL2n(R). Let Sκ(Γn) be the space of cusp forms of weight κ with respect to Γn on the quaternion half-space of degree n. We construct a lifting from primitive forms in Sk(SL2(Z)) to Sk+2n−2(Γn) and a lifting from primitive forms in Sk(Γ0(d)) to Sk+2(Γ2), where d is a factor of DH. These liftings are generalizations of the Maass lifting investigated by Krieg. |
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Keywords: | 11F55 11F30 |
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