Base change for the Saito-Kurokawa representations of PGSp(4)
type: Item
instance of: scholarly article
title: Base change for the Saito-Kurokawa representations of PGSp(4)
zbMATH Open document ID: 0652.10022
DOI: 10.1016/0022-314X(88)90004-2
author: I. I. Pyatetskii-Shapiro
author: James Cogdell
published in: Journal of Number Theory
publication date: 1988-01-01T00:00:00Z
review text: The Saito-Kurokawa representation of PGSp(4) are (local and automorphic) representations constructed by `lifting' from representations of PGL(2). They can also be directly characterized. The authors consider the behaviour of these representations under a base change K/k which is cyclic of prime degree q. The representations are naturally described in term of packets, and the number of cuspidal elements in a packet depends on whether the L-function of the original representation of PGL(2) vanishes at the centre of the critical strip. The size of the complete packet is known. The object of this investigation is to use these ideas to give examples for the `Langlands' philosophy'. In this case, when q is odd, the number of cuspidal representations increases, whereas when \(q=2\) it can happen that cuspidal representations transform under base change into non-cuspidal representations.
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 22E25
zbMATH DE Number: 4063194
zbMATH Keywords: Saito-Kurokawa representation
zbMATH Keywords: (local and automorphic) representations
zbMATH Keywords: base change
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
cites work: Q3328757
cites work: Base change for \(SL_ 2^{\sim}\)
cites work: Q3856974
cites work: Transcending Classical Invariant Theory
cites work: Automorphic forms on GL (2)
cites work: Q3049040
cites work: Q5622438
cites work: On the Saito-Kurokawa lifting
cites work: Q3325945
cites work: Q3904667
full work available at URL: 0022-314x(88)90004-2
OpenAlex ID: W2073075421
description: scientific article; zbMATH DE number 4063194