On the metaplectic analog of Kazhdan's ``endoscopic'' lifting
type: Item
instance of: scholarly article
title: On the metaplectic analog of Kazhdan's ``endoscopic'' lifting
zbMATH Open document ID: 0644.22010
DOI: 10.1007/BF02766205
published in: Israel Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let k'/k be a cyclic extension of degree r of number fields. Suppose that x \(n=1\) has n solutions in k. Let D be a division algebra of dimension r 2 over k. We let T (resp. \(G_ D)\) be the algebraic group so that for any k-algebra A one has \(T(A)=(A\otimes_ kk')^{\times}\) (resp. \(G_ D(A)=(A\otimes_ kD)^{\times})\). The endoscopic lifting of the title is a lifting of automorphic representations of \(T(k_ A)\) (i.e. Größencharaktere of k') to automorphic representations of \(GL_ r(k_ A)\). Let \(\tilde T\) (resp. \(\tilde G_ D)\) be suitable n-fold metaplectic covers of \(T(k_ A)\) (resp. \(G_ D(k_ A))\). Then under the assumption that k' splits D and various other technical assumptions the author proves a correspondence between automorphic representations of \(\tilde T\) and a well defined subset of those of \(\tilde G_ D\). This is done using a simple version of the Selberg trace formula.
Mathematics Subject Classification ID: 22E55
Mathematics Subject Classification ID: 11F70
zbMATH DE Number: 4049906
zbMATH Keywords: cyclic extension
zbMATH Keywords: number fields
zbMATH Keywords: division algebra
zbMATH Keywords: endoscopic lifting
zbMATH Keywords: lifting of automorphic representations
zbMATH Keywords: Größencharaktere
zbMATH Keywords: automorphic representations
zbMATH Keywords: metaplectic covers
zbMATH Keywords: Selberg trace formula
author: David Joyner
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4049906