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|
Bibliographical noteFunding Information:
The first named author is supported in part by (USA) NSF grant DMS-0400414. The main part of the work was carried out during his visit in the Institute of Mathematics of the Chinese Academy of Science, Beijing, where the second named author was working as a postdoctoral fellow. Both authors would like to thank the Institute for hospitality and support, which made this collaboration possible, and to thank the referee for thorough reading and useful comments and suggestions.