Classification of distinguished representations of GL(2)

2025/06/27 by Yuki Matsumoto, Matsumoto, Yuki
Mathematics · #11F70 #20G25 (Secondary) #22E50 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2506.22097

openalex publication_date 2025/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a non-archimedean local field with odd residual characteristic, and let H be a maximal torus of \rm GL₂(F). In this paper, we will classify the irreducible H-distinguished representations of \rm GL₂(F) by using Casselman's criteria for p-adic symmetric spaces developed by Kato-Takano.

Citations

• Square integrability of representations on p-adic symmetric spaces
• Subrepresentation Theorem for p-adic Symmetric Spaces

Related

• Non-admissible irreducible representations of p-adic GL_n in characteristic p
• Cuspidal representations of GL(n,F) distinguished by a maximal Levi subgroup, with F a non-archimedean local field
• Restriction of representations of metaplectic GL₂(F) to tori
• Generic representations of GL(n) over a p-adic field distinguished by a maximal Levi subgroup
• Coefficient systems and supersingular representations of GL₂(F)