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On a lifting problem of L-packets
Published online by Cambridge University Press: 14 July 2016
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 
$G$ .
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