Global liftings between inner forms of GSp(4) - Rösner, Mirko; Weissauer, Rainer (Journal of number theory, 2024)
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.
Online verfügbar: 17. Mai 2024, Artikelversion: 27. Mai 2024
Gesehen am 18.11.2024