Square Integrable Representations and the Standard Module Conjecture for General Spin Groups

http://dx.doi.org/10.4153/CJM-2009-033-3
Canad. J. Math. 61(2009), 617-640

  Published:2009-06-01
 Printed: Jun 2009

In this paper we study square integrable representations and $L$-functions for quasisplit general spin groups over a $p$-adic field. In the first part, the holomorphy of $L$-functions in a half plane is proved by using a variant form of Casselman's square integrability criterion and the Langlands--Shahidi method. The remaining part focuses on the proof of the standard module conjecture. We generalize Mui\'c's idea via the Langlands--Shahidi method towards a proof of the conjecture. It is used in the work of M. Asgari and F. Shahidi on generic transfer for general spin groups.