Generalized Shalika models of p-adic SO4n and functoriality

Abstract

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.