Journal
COMPOSITIO MATHEMATICA
Volume 156, Issue 11, Pages 2298-2367Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1112/S0010437X20007496
Keywords
Gan Gross Prasad conjectures; L-packets; A-packets; L-parameters; A-parameters; relevant pair of A-parameters; local branching laws; period integrals; central L-values; classical groups; L-functions; epsilon factors; representation theory
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Funding
- MOE Tier 2 grant [R146-000-233-112]
- Science and Engineering Research Board of the Department of Science and Technology, India through the JC Bose National Fellowship of the Government of India [JBR/2020/000006]
- Government of the Russian Federation [14.W03.31.0030]
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This paper generalizes the Gan-Gross-Prasad (GGP) conjectures that were earlier formulated for tempered or more generally generic L-packets to Arthur packets, especially for the non-generic L-packets arising from Arthur parameters. The paper introduces the key notion of a relevant pair of Arthur parameters that governs the branching laws for GL(n) and all classical groups over both local fields and global fields. It plays a role for all the branching problems studied in Gan et al. [Symplectic local root numbers, central critical L-values and restriction problems in the representation theory of classical groups. Sur les conjectures de Gross et Prasad. I, Asterisque 346 (2012), 1-109] including Bessel models and Fourier-Jacobi models.
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