Twisted GGP problems and conjectures. (English) Zbl 1532.11065
In their paper [Astérisque 346 (2012; Zbl 1257.22001)], the authors provided a study of a family of restriction problems for classical groups over both local and global fields. In a series of papers, authors proposed precise answers to problems of such type, based on the Langlands correspondence, and the considered problems were formulated in terms of a pair \(W \subset V\) consisting of orthogonal, Hermitian, or skew-Hermitian spaces.
In the paper under the review, the authors proceed one step further and consider a twisted variant of their conjectures for a pair \(W = V\) consisting of a pair of skew-Hermitian spaces. In particular, the non-tempered analog of the GGP conjectures in the twisted settings is obtained. The vanishing of the corresponding higher Ext groups for tempered representation is also shown.
In the paper under the review, the authors proceed one step further and consider a twisted variant of their conjectures for a pair \(W = V\) consisting of a pair of skew-Hermitian spaces. In particular, the non-tempered analog of the GGP conjectures in the twisted settings is obtained. The vanishing of the corresponding higher Ext groups for tempered representation is also shown.
Reviewer: Ivan Matić (Osijek)
MSC:
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
| 22E55 | Representations of Lie and linear algebraic groups over global fields and adèle rings |
Keywords:
branching laws; real and \(p\)-adic groups; classical groups; unitary groups; Weil representation; GGP conjectures; period integrals; skew-Hermitian spaces; Langlands parameters; tempered representationsCitations:
Zbl 1257.22001References:
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