On a lifting problem of L-packets

Bin Xu Department of Mathematics and Statistics, University of Calgary, Calgary, Canada

Representation Theory mathscidoc:2206.30005

Compositio Mathematica, 152, (9), 2016.7
Let G ⊆ \tilde{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 \tilde{G}. Motivated by this, we hope to construct the L-packets of \tilde{G} from those of G. The primary example in our mind is when G = 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 \tilde{G} = 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 \tilde{G} from those of G.
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  title={On a lifting problem of L-packets},
  author={Bin Xu},
  booktitle={Compositio Mathematica},
Bin Xu. On a lifting problem of L-packets. 2016. Vol. 152. In Compositio Mathematica. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220618163449911713411.
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