Joint IAS/Princeton University Number Theory Seminar

The endoscopy theory provides a large class of examples of Langlands functoriality, and it also plays an important role in the classification of automorphic forms. The central part of this theory are some conjectural identities of Harish-Chandra characters between a reductive group and its endoscopic groups. Such identities are established in the real case by Shelstad, but they are still largely unknown in the p-adic case due to our limited knowledge of characters in this case. Arthur uses certain (twisted) stable trace formulas to establish the character identities for symplectic groups and orthogonal groups in the p-adic case. In this talk, I will explain how to extend Arthur's character identities to the similitude groups by using some other cases of the twisted stable trace formula. So our work is an application of the long project of Moeglin and Waldspurger, which establishes the twisted stable trace formula in the general case.