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.

We give a survey on Mœglin's construction of representations in the Arthur packets for p-adic quasisplit symplectic and orthogonal groups. The emphasis is on comparing Mœglin's parametrization of elements in the Arthur packets with that of Arthur.

Zelevinsky’s classification theory of discrete series of p-adic general linear groups has been well known. Mœglin and Tadić gave the same kind of theory for p-adic classical groups, which is more complicated due to the occurrence of nontrivial structure of L-packets. Nonetheless, their work is independent of the endoscopic classification theory of Arthur (also Mok in the unitary case), which concerns the structure of L-packets in these cases. So our goal in this paper is to make more explicit the connection between these two very different types of theories. To do so, we reprove the results of Mœglin and Tadić in the case of quasisplit symplectic groups and orthogonal groups by using Arthur’s theory.