2024/02/05 by Jeffrey Adams, Adams, Jeffrey, Alexandre Afgoustidis +1
Mathematics · #20G05 #22E47 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2402.03552
openalex publication_date 2024/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider the irreducible representations of a real reductive group G(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(ℝ) of G(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.