Mathematical Research Letters

Volume 19 (2012)

Number 4

On the local and global exterior square $L$-functions of $GL_n$

Pages: 785 – 804

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n4.a5

Authors

Pramod Kumar Kewat (Department of Applied Mathematics, Indian School of Mines, Dhanbad, India)

Ravi Raghunathan (Department of Mathematics, Indian Institute of Technology, Bombay, India)

Abstract

We show that the local exterior square $L$-functions of $GL_n$ constructed via the theory of integral representations by Jacquet and Shalika coincide with those constructed by the Langlands–Shahidi method for square integrable representations (and for all irreducible representations when $n$ is even). We also deduce several local and global consequences.

Keywords

exterior square L-functions

2010 Mathematics Subject Classification

11F70

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