On a lifting problem of L-packets

Abstract

Let $G\subseteq \tilde{G}$ be two quasisplit connected reductive groups over a local field of characteristic zero and $G_{der}={\tilde{G}}_{der}$. 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 that of $\tilde{G}$. Motivated by this, we hope to construct the L-packets of $\tilde{G}$ from that of $G$. The primary example in our mind is when $G=Sp(2n)$, whose L-packets have been determined by Arthur (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 that of $G$.

To appear in Compositio Mathematica

References in corpus (1)

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups

Cited by in corpus (6)

• L-packets of quasisplit $GSp(2n)$ and $GO(2n)$
• Langlands parameters, functoriality and Hecke algebras
• Arthur's multiplicity formula for GSp${}_4$ and restriction to Sp${}_4$
• Galois representations for even general special orthogonal groups
• The Exterior Cubic L-function of GU(6) and Unitary Automorphic Induction
• Arthur packets for quasisplit $GSp(2n)$ and $GO(2n)$ over a $p$-adic field