The non-tempered θ10 Arthur parameter and Gross-Prasad conjectures

Nadya Gurevich, Dani Szpruch

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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.

Original languageEnglish
Pages (from-to)372-426
Number of pages55
JournalJournal of Number Theory
StatePublished - 1 Aug 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.


  • Gross-Prasad conjectures
  • Non-tempered arthur parameter
  • Theta correspondence


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