Representations of reductive groups over local fields

Abstract

We discuss progress towards the classification of irreducible admissible representations of reductive groups over non-archimedean local fields and the local Langlands correspondence. We also state some (partly conjectural) compatibility properties of the refined local Langlands correspondence.

Hecke algebras for p-adic reductive groups and Local Langlands Correspondences for Bernstein blocks

“…We expect that the bijection L from (1.0.5) satisfies the desired properties of the local Langlands correspondence, which include the properties described in [AP22, Definition 3.25] and in [Kal22], and hence provides new cases of the latter.…”