Saved in:
Bibliographic Details
Main Authors: Adams, Jeffrey, Afgoustidis, Alexandre
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.03552
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • Consider the irreducible representations of a real reductive group $G(\mathbb{R})$, and their parametrization by the local Langlands correspondence. We ask: does the parametrization give easily accessible information on the restriction of representations to a maximal compact subgroup $K(\mathbb{R})$ of $G(\mathbb{R})$? We find a natural connection between the set of lowest $K$-types of a representation and its Langlands parameters. For our results, it is crucial to use the refined version of the local Langlands correspondence, involving (coverings of) component groups attached to $L$-homomorphisms. The first part of the paper is a simplified description of this refined parametrization.