Twisted endoscopy and the generic packet conjecture

We prove a twisted analogue of the result of Rodier and Moeglin-Waldspurger on the dimension of the space of degenerate Whittaker vectors. This allows us to prove that certain twisted endoscopy forGL(n) implies the (local) generic packet conjecture for many classical groups. Partially supported by the Grants-in-Aid for Scientific Research No. 12740018, the Ministry of Education, Science, Sports and Culture, Japan.