The non-tempered theta 10 Arthur parameter and Gross-Prasad Conjectures
Number Theory
2014-09-17 v2
Abstract
We provide a construction of local and automorphic non-tempered Arthur packets of the group SO(3,2) and its inner form SO(4,1) associated with a certain Arthur's parameter and prove a multiplicity formula. We further study the restriction of the representations in these packets 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) x SO(3,1) and SO(3,2) x SO(3,1) for the representations above. The main tool is the local and global theta correspondence for unitary quaternionic similitude dual pairs.
Keywords
Cite
@article{arxiv.1310.4187,
title = {The non-tempered theta 10 Arthur parameter and Gross-Prasad Conjectures},
author = {Nadya Gurevich and Dani Szpruch},
journal= {arXiv preprint arXiv:1310.4187},
year = {2014}
}