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On a lifting problem of L-packets

Part of: Discontinuous groups and automorphic forms Lie groups

Published online by Cambridge University Press:  14 July 2016

Bin Xu
Bin Xu*
Affiliation:
Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada, T2N 1N4 email bin.xu2@ucalgary.ca
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Abstract

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Let $G\subseteq \widetilde{G}$ be two quasisplit connected reductive groups over a local field of characteristic zero and having the same derived group. Although the existence of L-packets is still conjectural in general, it is believed that the L-packets of $G$ should be the restriction of those of $\widetilde{G}$. Motivated by this, we hope to construct the L-packets of $\widetilde{G}$ from those of $G$. The primary example in our mind is when $G=\text{Sp}(2n)$, whose L-packets have been determined by Arthur [The endoscopic classification of representations: orthogonal and symplectic groups, Colloquium Publications, vol. 61 (American Mathematical Society, Providence, RI, 2013)], and $\widetilde{G}=\text{GSp}(2n)$. As a first step, we need to consider some well-known conjectural properties of L-packets. In this paper, we show how they can be deduced from the conjectural endoscopy theory. As an application, we obtain some structural information about L-packets of $\widetilde{G}$ from those of $G$.

Keywords

quasisplit reductive groupsendoscopic transferL-packets

MSC classification

Primary: 22E50: Representations of Lie and linear algebraic groups over local fields
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 9 , September 2016 , pp. 1800 - 1850
Copyright
© The Author 2016 

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