Whittaker spaces for reducible unitary principal series representations of \widetildeSL₂(F)

2024/11/18 by Dani Szpruch, Szpruch, Dani
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2411.11460

openalex publication_date 2024/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a p-adic field containing the full group of n^th roots of 1 and let \widetildeSL₂(F) be the n-fold cover of SL₂(F) constructed by Kubota. In this paper we compute the dimension of the space of Whittaker functionals of the two irreducible summands inside a reducible unitary genuine principal series representation of \widetildeSL₂(F). We also show how these dimensions change when the Whittaker character is modified. As an application we determine the action of the twisted Kazhdan-Patterson n-fold cover of GL₂(F) on the two summands. We emphasize that our main results addresses both ramified and unramified representations and do not rely on the assumption that the cover is tame.

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