We introduce the generalized Shalika model for SO(4n), the split even orthogonal group of rank 2n, and develop the local and global compatibilities with the Shalika model for GL(2n), the general linear group of rank 2n. As result, we determine the existence of poles of certain Eisenstein series on SO(4n) in terms of the Shalika model on the cuspidal datum (GL(2n), π), and give a different proof for the determination of the pole at s = 1 of the exterior square L-function L(s, π,Λ2) in terms of the Shalika model on π.
|Original language||English (US)|
|Number of pages||33|
|Journal||Journal of the Ramanujan Mathematical Society|
|State||Published - Jun 2007|