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On descent and the generic packet conjecture

Sandeep Varma
From the journal Forum Mathematicum

Abstract

Suppose F is a p-adic field, and H1 is (a z-extension of) a group that is twisted endoscopic to a connected reductive quasi-split group G over F. Suppose G satisfies the strong form of the generic packet conjecture (also called tempered packet conjecture in literature). Under certain assumptions, we show that the twisted endoscopic character identities associated to this situation imply the strong form of the generic packet conjecture for H1. This generalizes a result of T. Konno, and lets us deduce, under the assumption that appropriate character identities are satisfied, the generic packet conjecture for general spin (GSpin) groups.

MSC 2010: 22E50

Communicated by Freydoon Shahidi


Acknowledgements

The contents of this paper are partly based on the author’s thesis, [32], done a few years ago under the guidance of Professor Freydoon Shahidi. I am very grateful to Professor Shahidi for suggesting the problem of proving the generic packet conjecture in its stronger as well as more general form (under suitable assumptions), and for patient guidance and encouragement. This work and I have benefited a lot from the guidance and encouragement of Professors D. Goldberg and J.-K. Yu. I also gratefully acknowledge useful communication and encouragement from Professors D. Prasad and R. Kottwitz. I am thankful to Dr. R. Ganapathy, for it was joint work with her that motivated me to write this paper up. I thank Professor J.-L. Waldspurger for kindly clarifying some points over an email. I thank the referee for a careful and thorough reading of this article and for pointing out several omissions.

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Received: 2015-6-11
Revised: 2015-10-30
Published Online: 2016-5-5
Published in Print: 2017-1-1

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