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International Mathematics Research Papers (2005) 2005:1-52, doi:10.1155/IMRP.2005.1
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Copyright © 2005 Hindawi Publishing Corporation. All rights reserved.

Stable base change lift from unitary groups to GLN

Henry H. Kim and Muthukrishnan Krishnamurthy

The main purpose of this paper is to establish the existence of the stable base change transfer of globally generic cuspidal representations of the quasisplit unitary group to the appropriate general linear group. It is based on the Langlands-Shahidi method and the converse theorem of Cogdell and Piatetski-Shapiro. The main result says that the base change is the isobaric sum of (unitary) cuspidal representations of smaller general linear groups such that their Asai L-functions have a pole at s=1. We also construct the local components of the transfer explicitly, using the classification of discrete series due to Mœglin and Tadic and generic nontempered representations due to Muic. The paper concludes with applications toward the generalized Ramanujan conjecture and the holomorphy of the normalized local intertwining operators.


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