On a cubic lifting
type: Item
instance of: scholarly article
title: On a cubic lifting
zbMATH Open document ID: 0954.11017
DOI: 10.1007/BF02780174
author: Zhengyu Mao
author: Steve Rallis
published in: Israel Journal of Mathematics
publication date: 2001-02-12T00:00:00Z
review text: The cubic lifting in the title is a correspondence between automorphic representations of \(G = \text{SL}_2\) over a number field containing the cubic roots of unity and automorphic representations of the three-fold cover \(\widetilde G\) of \(G\). This lifting is defined and studied in \textit{D. Ginzburg, S. Rallis, D. Soudry} [Am. J. Math. 119, 251-335 (1997; Zbl 0877.11031)]. The present paper completes [loc. cit.] by showing that any irreducible cuspidal representation of \(\widetilde G\) has a cubic lift to \(G\). This is done by a now well-known method, namely by establishing and exploiting a relative trace formula.
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 1389705
zbMATH Keywords: cubic lifting
zbMATH Keywords: automorphic representations
zbMATH Keywords: three-fold cover
zbMATH Keywords: cuspidal representation
zbMATH Keywords: relative trace formula
reviewed by: J. G. M. Mars
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02780174
OpenAlex ID: W1969953719
description: scientific article; zbMATH DE number 1389705