On certain automorphic descents to GL2

David Ginzburg, Dihua Jiang, David Soudry

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We consider a new construction of automorphic representations of GL2(A), using the general idea of automorphic descent methods. In particular, four families of examples are considered. The representations τ of GL2(A) are obtained from automorphic representations π on reductive groups H, which contain a reductive subgroup G of GSp2n. We give criteria for nonvanishing and for cuspidality of the constructed representations τ, in terms of periods or co-periods and by the holomorphy at s=1 of certain l-functions of π. We also calculate the relation of the unramified parameters in certain cases, which indicates that τ and π fit partially to the Langlands functorial principle. We prove some low-rank cases to support our conjectures.

Original languageEnglish (US)
Pages (from-to)4779-4820
Number of pages42
JournalInternational Mathematics Research Notices
Issue number21
StatePublished - Oct 31 2011

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