Quaternionic symplectic model for discrete series representations

2025/07/22 by Nadir Matringe, Matringe, Nadir, Miyu Suzuki +1
Computer Science · Mathematics · #11F70 #22E50 #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2507.16364

openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let D be the quatenion division algebra over a non-Archimedean local field F of characteristic zero and odd residual characterisitc. We show that an irreducible discrete series representation of GL_n(D) is Sp_n(D)-distinguished only if it is supercuspidal. Here, Sp_n(D) is the quaternionic symplectic group. Combined with the recent study on Sp_n(D)-distinguished supercuspidal representations by Sécherre and Stevens, this completes the classification of Sp_n(D)-distinguished discrete series representations, as predicted by Dipendra Prasad.

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