On principal series representations of quasi-split reductive p-adic groups
arXiv:2304.06418 · doi:10.2140/pjm.2025.334.269
Abstract
Let G be a quasi-split reductive group over a non-archimedean local field. We establish a local Langlands correspondence for all irreducible smooth complex G-representations in the principal series. The parametrization map is injective, and its image is an explicitly described set of enhanced L-parameters. Our correspondence is determined by the choice of a Whittaker datum for G, and it is canonical given that choice. We show that our parametrization satisfies many expected properties, among others with respect to the enhanced L-parameters of generic representations, temperedness, cuspidal supports and central characters. Along the way we characterize genericity in terms of representations of an affine Hecke algebra.
New in version 2: results about the independence of the choice of s_T in its Weyl group orbit