The endoscopic classification for metaplectic groups
I will give a summary discussion of a classification of the automorphic discrete spectrum of the metaplectic group Mp(2n) in the style of Arthur’s conjecture. Starting with the pioneering work of Waldspurger, who treated the case of Mp(2) via theta correspondence with SO(3) ,we will discuss the development of a theory of endoscopy for Mp(2n) by Adams, Renard and Wenwei Li and the extension of theta correspondence techniques to Mp(2n), via the work of Adams-Barbasch, Gan-Savin and Gan-Ichino. Finally the theory of endoscopy and the theta correspondence approach are reconciled through the work of Caihua Luo and Wenwei Li, via the stable trace formula for Mp(2n). In this story, the work of Arthur on the automorpihc discrete spectrum of classical groups is a crucial input.