Let F denote a p-adic local field of characteristic zero. In this paper, we investigate the structures of irreducible admissible representations of SO4n(F) having nonzero generalized Shalika models and find relations between the generalized Shalika models and the local Arthur parameters, which support our conjectures on the local Arthur parametrization and the local Langlands functoriality in terms of the dual group associated to the spherical variety, which is attached to the generalized Shalika models.
Bibliographical noteFunding Information:
∗The work of the first-named author is supported in part by NSF (USA) grant DMS-0653742 and DMS-1001672, and by The Chinese Academy of Sciences. The second-named author is supported by NSC 99-2115-M-006-007-and NCTS Tai-wan. The third-named author is supported partly by the program PCSIRT (Pro-gram for Changjiang Scholars and Innovative Research Team) in East China Nor-mal University. All three authors are supported in part by NSFC 10701034, P.R.China. The authors would like to thank The Morningside Center of Math-ematics and the Institute of Mathematics, CAS, for strong support through the summer program over the years. Received November 5, 2010 and in revised form October 12, 2011