A refinement of the Adams’ conjecture on theta correspondence
Date:
SCMS Number Theory Seminar, Shanghai, China
Abstract: Theta correspondence is an enigmatic but powerful tool in the study of the Langlands program. The Adams’ conjecture on theta correspondence described it in terms of A-parameters. In this talk, we will propose a refined version of the Adams’ conjecture, which also describes the parametrizations inside A-packets, and prove it in the stable range case. We will also exhibit some applications, like: 1. the Arthur’s multiplicity formula for non quasi-split classical groups; 2. some special cases of the twisted Gan-Gross-Prasad conjecture. If time permits, we will also talk about some potential applications to metaplectic groups. These are based on a joint work with Jialiang Zou and a joint work with Wee Teck Gan.
Related works: Arthur’s multiplicity formula, Theta and A-packets, Some cases of twisted GGP.