Standard modules and intertwining operators for reductive p-adic groups

Abstract

Consider a reductive group G over a non-archimedean local field. The Galois group Gal(C/Q) acts naturally on the category of smooth complex G-representations. We prove that this action stabilizes the class of standard modules. This generalizes and relies on an analogous result about essentially square-integrable representations. Other important objects in the proof of our main result are intertwining operators between parabolically induced G-representations, and the associated Harish-Chandra μ-functions. We determine an explicit formula for the μ-function of any irreducible representation of any Levi subgroup of G.