Abstract

The local Langlands correspondence for a classical group over a nonarchimedean local field, now a theorem of Arthur (and others) in characteristic zero, predict a surjective map from irreducible (smooth complex) representations of the group to Langlands parameters, with finite fibres. We consider the question of making this map explicit for symplectic groups G: given a cuspidal irreducible representation, we are able to describe the corresponding Langlands parameter up to unramified characters in general (and, in certain cases, completely). As a result, we deduce an explicit ``wild transfer’’ map for endoscopic transfer to a general linear group or, equivalently, a map from ``endo-parameters for G’’ to wild parameters (the restriction to wild inertia of Langlands parameters) which is compatible with the Langlands correspondence. It seems likely that this is part of a more general theory of ``endo-parameters’’, compatible with endoscopy, and that a refined version of these wild parameters will also partially distinguish between elements in an L-packet. Joint work with Blondel, Henniart, Kurinczuk, Skodlerack.