Smooth Duals of Inner Forms of $GL_n$ and $SL_n$
Representation Theory
2020-09-08 v2
Abstract
Let be a non-archimedean local field. We prove that every Bernstein component in the smooth dual of each inner form of the general linear group is canonically in bijection with the extended quotient for the action, given by Bernstein, of a finite group on a complex torus. For inner forms of we prove that each Bernstein component is canonically in bijection with the associated twisted extended quotient. In both cases, the bijections satisfy naturality properties with respect to the tempered dual, parabolic induction, central character, and the local Langlands correspondence.
Keywords
Cite
@article{arxiv.1505.04361,
title = {Smooth Duals of Inner Forms of $GL_n$ and $SL_n$},
author = {Anne-Marie Aubert and Paul Baum and Roger Plymen and Maarten Solleveld},
journal= {arXiv preprint arXiv:1505.04361},
year = {2020}
}