Arthur packets for Mp(2n) and a multiplicity formula

BIMSA-YMSC Tsinghua Number Theory Seminar

Organizers：

Hansheng Diao, Heng Du, Yueke Hu, Bin Xu, Yihang Zhu

Speaker：

Wen-Wei Li (BICMR / Peking University)

Time：

Mon., 10:00-11:00 am, Nov. 11, 2024

Venue：

C654, Shuangqing Complex Building A

Title：

Arthur packets for Mp(2n) and a multiplicity formula

Abstract:

Let Mp(2n, F) be the metaplectic covering of the symplectic group Sp(2n, F) over a local field F of characteristic zero. The Arthur packets of genuine irreducible representations of Mp(2n, F) are defined in terms of endoscopic transfer from products of odd orthogonal groups. In the global setting, they give rise to a multiplicity formula for the discrete genuine automorphic spectrum of Mp(2n, A) à la Arthur, with an extra global root number. I will try to explain the global-to-local proof, which combines the stable trace formula for Mp(2n, A), the results of Gan and Ichino based on theta liftings, as well as the recent works of Luo and Liu-Lo-Shahidi. This is based on arXiv:2410.13606.