Construction of Steinberg type representations for reductive \(p\)-adic groups
type: Item
instance of: scholarly article
title: Construction of Steinberg type representations for reductive \(p\)-adic groups
zbMATH Open document ID: 1123.22010
author: Goran Muić
published in: Mathematische Zeitschrift
publication date: 2006-11-09T00:00:00Z
review text: Let \(F\) be a nonarchimedean field and \(G\) the group of \(F\)-points of a connected reductive group over \(F\). This paper gives a construction of certain discrete series representations of \(G\). The author generalizes and refines the method of Tadić for the construction of some discrete series representations of classical \(p\)-adic groups. The method relies on Jacquet module techniques and in this paper it is extended to a general reductive \(p\)-adic group. The author first defines representations of Steinberg type. These representations are defined in families. A family contains representations of different Levi subgroups of \(G\) and they are related to each other via a certain condition on the Jacquet modules. The author then develops a method for constructing such representations and to compute explicitly their Jacquet modules.
reviewed by: Dubravka Ban
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 22E35
zbMATH DE Number: 5071449
zbMATH Keywords: Steinberg type representations
zbMATH Keywords: discrete series representations
zbMATH Keywords: Jacquet modules
MaRDI profile type: Publication
full work available at URL: s00209-006-0946-6
OpenAlex ID: W2143543084
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DOI: 10.1007/S00209-006-0946-6
description: scientific article; zbMATH DE number 5071449