Generic irreducibility of parabolic induction for real reductive groups
Abstract
Let be a real reductive linear group in the Harish-Chandra class. Suppose that is a parabolic subgroup of with Langlands decomposition . Let be an irreducible representation of the Levi factor . We give sufficient conditions on the infinitesimal character of for the induced representation to be irreducible. In particular, we prove that if is an irreducible representation of , then for a generic character of , the induced representation is irreducible. Here the parameter is in and generic means outside a countable, locally finite union of hyperplanes which depends only on the infinitesimal character of . Notice that there is no other assumption on or than being irreducible, so the result is not limited to generalised principal series or standard representations, for which the result is already well known.
Cite
@article{arxiv.2310.11202,
title = {Generic irreducibility of parabolic induction for real reductive groups},
author = {David Renard},
journal= {arXiv preprint arXiv:2310.11202},
year = {2024}
}
Comments
18 pages, version 3, typos, mistakes and omissions corrected, references added, statements of the main results reformulated