We provide a construction of local and automorphic non-tempered Arthur packets AΨ of the group SO(3, 2) and its inner form SO(4, 1) associated with Arthur's parameterΨ:LF×SL2(C)→O2(C)×SL2(C)→Sp4(C) and prove a multiplicity formula. We further study the restriction of the representations in AΨ to the subgroup SO(3, 1). In particular, we discover that the local Gross-Prasad conjecture, formulated for generic L-packets, does not generalize naively to a non-generic A-packet. We also study the non-vanishing of the automorphic SO(3, 1)-period on the group SO(4, 1)×SO(3, 1) and SO(3, 2)×SO(3, 1) for the representations above. The main tool is the local and global theta correspondence for unitary quaternionic similitude dual pairs.
Bibliographical notePublisher Copyright:
© 2015 Elsevier Inc.
- Gross-Prasad conjectures
- Non-tempered arthur parameter
- Theta correspondence