Global liftings between inner forms of GSp(4)
For reductive groups G over a number field we discuss automorphic liftings of cohomological cuspidal irreducible automorphic representations π of G(A) to irreducible cohomological automorphic representations of H(A) for the quasi-split inner form H of G, and other inner forms as well. We show the ex...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
October 2024
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| In: |
Journal of number theory
Year: 2024, Volume: 263, Pages: 79-138 |
| ISSN: | 1096-1658 |
| DOI: | 10.1016/j.jnt.2024.04.010 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1016/j.jnt.2024.04.010 Verlag, kostenfrei, Volltext: https://www.sciencedirect.com/science/article/pii/S0022314X24001173 
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| Author Notes: | Mirko Rösner, Rainer Weissauer |
MARC
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| 520 | |a For reductive groups G over a number field we discuss automorphic liftings of cohomological cuspidal irreducible automorphic representations π of G(A) to irreducible cohomological automorphic representations of H(A) for the quasi-split inner form H of G, and other inner forms as well. We show the existence of nontrivial weak global cohomological liftings in many cases, in particular for the case where G is anisotropic at the archimedean places. A priori, for these weak liftings we do not give a description of the precise nature of the corresponding local liftings at the ramified places, nor do we characterize the image of the lifting. For inner forms of the group H=GSp(4) however we address these finer questions. Especially, we prove the recent conjectures of Ibukiyama and Kitayama on paramodular newforms of square-free level. | ||
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