Supercuspidal L-packets

TL;DR

This paper constructs explicit supercuspidal L-packets for reductive groups over non-archimedean fields, linking Langlands parameters to irreducible representations and providing evidence for the local Langlands correspondence.

Contribution

It explicitly associates supercuspidal representations to discrete Langlands parameters for certain reductive groups, clarifying the internal structure of L-packets.

Findings

Explicit construction of supercuspidal L-packets

Relation between L-packets and centralizers of parameters

Evidence supporting the local Langlands correspondence

Abstract

Let F be a non-archimedean local field and let G be a connected reductive group defined over F. We assume that G splits over a tame extension of F and that the residual characteristic p does not divide the order of the Weyl group. To each discrete Langlands parameter of the Weil group of F into the complex L-group of G we associate explicitly a finite set of irreducible supercuspidal representations of G(F), and relate its internal structure to the centralizer of the parameter. We give evidence that this assignment is an explicit realization of the local Langlands correspondence.