A unipotent representation associated with a minimal orbit: The \(so(4,3)\) case
type: Item
instance of: scholarly article
title: A unipotent representation associated with a minimal orbit: The \(so(4,3)\) case
zbMATH Open document ID: 0849.22016
author: Hervé Sabourin
published in: Journal of Functional Analysis
publication date: 1996-06-30T00:00:00Z
review text: \textit{D. Vogan} [Invent. Math. 116, 677-791 (1994; Zbl 0808.22003)] has proved the existence of an element \(\pi\) of the unitary dual of the universal covering of \(\text{SO}_0(4,3)\) of which the annihilator is the Joseph ideal. In this work, we present a new method for obtaining this result, which essentially uses a parametrization of the unitary dual of a real almost semialgebraic group, given by \textit{M. Duflo} [Acta Math. 149, 153-213 (1982; Zbl 0529.22011)]. Then, we give an explicit realization of \(\pi\) in \(L^2(\mathbb{R}^3 \times \mathbb{R}^*)\), we find the Langlands parameters and, at last, we study its restriction to \(G_2\).
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 880570
zbMATH Keywords: orbit methods
zbMATH Keywords: unitary dual
zbMATH Keywords: universal covering
zbMATH Keywords: annihilator
zbMATH Keywords: Joseph ideal
zbMATH Keywords: Langlands parameters
MaRDI profile type: Publication
full work available at URL: jfan.1996.0052
OpenAlex ID: W2076840988
DOI: 10.1006/JFAN.1996.0052
description: scientific article; zbMATH DE number 880570