Distinguished dihedral representations of GL(2) over a p-adic field

2006/10/24 by Nadir Matringe, Matringe, Nadir
Mathematics · #11S31 #11S37 #20G05 #20G30 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT #msc:11S31 #msc:11S37 #msc:20G05 #msc:20G30

paper · pdf · doi:10.48550/arxiv.math/0610724

Ce document contient 13 pages

openalex publication_date 2006/10/24 · arxiv created 2006/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a finite extension of ℚ _p. Any dihedral supercuspidal representation of GL _2 (K) arises from an admissible multiplicative character ω of a quadratic extension L of K. We show that such a representation is distinguished for GL _2 (F) if and only if L biquadratic over F and ω restricted to invertibles of one of the two other quadratic extensions of F in L is trivial. We then observe a similar statement for the principal series and we study all dihedral representations.

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