A Note on L-packets

One of the fundamental problems of local harmonic analysis is to classify the set Π(G) of equivalence classes of irreducible representations of G(F ). The problem separates naturally into two parts. The first is to establish the local Langlands correspondence. This conjecture of Langlands asserts that Π(G) is a disjoint union of finite subsets Πφ, indexed by (equivalence classes of) Langlands parameters φ for G. The sets Πφ are called L-packets, since their constituents could then be equipped with a common set of L-functions and e-factors, by the constructions of [T, §3–4] and [B, §12]. The second part of the problem is to classify the representations in a given packet Πφ. One would like to characterize them directly in terms of data attached to φ.