The local Ginzburg-Rallis model for generic representations
type: Item
instance of: scholarly article
title: The local Ginzburg-Rallis model for generic representations
zbMATH Open document ID: 1407.22008
author: Chen Wan
published in: Journal of Number Theory
publication date: 2019-01-23T00:00:00Z
review text: This paper presents a continuation of the author's works on the local Ginzburg-Rallis model for generic representations in the \(p\)-adic and the real case. Let \(\chi\) denote a character of \(F^{\times}\), where \(F\) is either a \(p\)-adic field or the field of the real numbers. In that model, to an irreducible admissible representation \(\pi\) of \(\mathrm{GL}(6, F)\) with central character \(\chi^{2}\), one associates a certain Hom space, the dimension of which is denoted by \(m(\pi)\). Furthermore, to an irreducible admissible representation \(\pi_D\) of \(\mathrm{GL}(3, D)\), where \(D\) is the unique quaternion algebra over \(F\), with central character \(\chi^{2}\), one can also associate a certain Hom space, the dimension of which is denoted by \(m(\pi_D)\). It is known that \(0 \leq m(\pi), m(\pi_D) \leq 1\). In the paper under the review, the author proves that for an irreducible generic representation \(\pi\) with central character \(\chi^{2}\) and the local Jacquet-Langlands correspondence \(\pi_D\) of \(\pi\) to \(\mathrm{GL}(3, D)\), we have \(m(\pi) + m(\pi_D) = 1\).
reviewed by: Ivan Matić
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 7005762
zbMATH Keywords: Ginzburg-Rallis model
zbMATH Keywords: generic representations
zbMATH Keywords: multiplicity one
MaRDI profile type: Publication
full work available at URL: j.jnt.2018.10.004
OpenAlex ID: W2901644488
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DOI: 10.1016/J.JNT.2018.10.004
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description: scientific article; zbMATH DE number 7005762