\(R\)-groups for unitary principal series of \textit{Spin} groups
type: Item
instance of: scholarly article
title: \(R\)-groups for unitary principal series of \textit{Spin} groups
zbMATH Open document ID: 1472.22009
author: Dubravka Ban
author: Kwangho Choiy
author: David Goldberg
published in: Journal of Number Theory
publication date: 2021-06-07T00:00:00Z
review text: In the paper under the review, the authors study the Knapp-Stein \(R\) group for unitary principal series of split spinor groups defined over a \(p\)-adic field \(F\). Let \(T\) denote a maximal \(F\)-split torus of the spinor group \(\mathrm{Spin}_m\), and let \(\widetilde{T}\) denote a maximal \(F\)-split torus of \(\mathrm{GSpin}_m\) such that \(T = \widetilde{T} \cap \mathrm{Spin}_m\) (we note that \(\mathrm{Spin}_m\) is a derived subgroup of \(\mathrm{GSpin}_m\)). Let \(\widetilde{\chi}\) denote a unitary character of \(\widetilde{T}\), and let \(\chi\) be the restriction of \(\widetilde{\chi}\) to \(T\). Let \(R\widetilde{\chi}\) and \(R_{\chi}\) stand for the Knapp-Stein \(R\)-groups for the principal series induced from \(\widetilde{\chi}\) and \(\chi\), respectively. Author obtain a complete description of the splitting of the exact sequence \[0 \rightarrow R\widetilde{\chi} \rightarrow R_{\chi} \rightarrow R_{\chi} / R\widetilde{\chi} \rightarrow 0.\] Also, the multiplicity one theorem in the restriction of irreducible tempered non-discrete series of \(\mathrm{GSpin}_m\) to \(\mathrm{Spin}_m\) is proved. Finally, following the Keys work on \(R\)-groups, authors prove Arthur's conjecture on \(R\)-groups for the unitary principal series of quasi-split groups over \(F\).
reviewed by: Ivan Matić
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 22E35
zbMATH DE Number: 7355819
zbMATH Keywords: \(R\)-groups
zbMATH Keywords: Arthur's conjecture
zbMATH Keywords: unitary principal series
zbMATH Keywords: \textit{Spin} group
MaRDI profile type: Publication
full work available at URL: j.jnt.2021.01.017
OpenAlex ID: W3130997963
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DOI: 10.1016/J.JNT.2021.01.017
description: scientific article; zbMATH DE number 7355819