Explicit description of irreducible \(\mathrm{GL}_2(\mathbb{Q}_p)\)-representations over \(\bar {\mathbf F}_{p}\)
type: Item
instance of: scholarly article
title: Explicit description of irreducible \(\mathrm{GL}_2(\mathbb{Q}_p)\)-representations over \(\bar {\mathbf F}_{p}\)
zbMATH Open document ID: 1239.22012
author: Stefano Morra
published in: Journal of Algebra
publication date: 2012-02-25T00:00:00Z
review text: In this paper, a description of irreducible mod \(p\) representations of \(\mathrm{GL}_2(\mathbb{Q}_p)\) using their socle filtration as \(\mathrm{GL}_2(\mathbb{Z}_p)\mathbb{Q}_p^\times\)-representations is given. This is done through the study of certain functions on the Bruhat-Tits tree. This allows one to describe the elements fixed by the congruence subgroups of \(\mathrm{GL}_2(\mathbb{Z}_p)\) which has been pursued in a different paper of the author [Invariant elements under some congruence subgroups for irreducible \(\mathrm{GL}_2(\mathbb{Q}_p)\)-representations over \(\overline{\mathbb{F}_p}\), preprint (2009)]. The techniques of the present paper generalize to unramified extensions of \(\mathbb{Q}_p\) giving the Iwahori structure for the canonical Hecke operators in terms of euclidean structures, see [the author, J. Algebra 339, No. 1, 252--303 (2011; Zbl 1239.22012)].
reviewed by: Gergely Zábrádi
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 11F85
zbMATH DE Number: 6009306
zbMATH Keywords: \(p\)-adic Langlands correspondence
zbMATH Keywords: Bruhat-Tits tree
zbMATH Keywords: socle filtration
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2011.02.043
OpenAlex ID: W166701170
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DOI: 10.1016/J.JALGEBRA.2011.02.043
description: scientific article; zbMATH DE number 6009306