## Abstract

We provide a construction of local and automorphic non-tempered Arthur packets A_{Ψ} 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 A_{Ψ} 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 language | English |
---|---|

Pages (from-to) | 372-426 |

Number of pages | 55 |

Journal | Journal of Number Theory |

Volume | 153 |

DOIs | |

State | Published - 1 Aug 2015 |

### Bibliographical note

Funding Information:The first author is partially supported by ISF grant 1691/10 . We thank W.T. Gan for his help and attention. We would like also to thank the referee for valuable remarks.

Publisher Copyright:

© 2015 Elsevier Inc.

## Keywords

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

## Fingerprint

Dive into the research topics of 'The non-tempered θ_{10}Arthur parameter and Gross-Prasad conjectures'. Together they form a unique fingerprint.