On certain Iwahori representations of unramified U(2, 1) in characteristic p

2017/06/08 by Peng Xu, Xu, Peng
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1706.02674

openalex publication_date 2017/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a non-archimedean local field of odd residue characteristic p. Let G be the unramified unitary group U(2, 1)(E/F), and K be a maximal compact open subgroup of G. For an F_p-smooth representation π of G containing a weight σ of K, we follow the work of Hu (\citeHu12) to attach π a certain I_K-subrepresentation, where I_K is the Iwahori subgroup in K. In terms of such an I_K-subrepresentation, we prove a sufficient condition for π to be non-finitely presented. We determine such an I_K-subrepresentation explicitly, when π is either a spherical universal Hecke module or an irreducible principal series.

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