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Modularity of hypertetrahedral representations

Martin, Kimball (2004) Modularity of hypertetrahedral representations. Comptes Rendus Mathematique, 339 (2). pp. 99-102. ISSN 1631-073X. doi:10.1016/j.crma.2004.05.003.

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Let F be a number field, G_F its absolute Galois group, and ρ: G_F → GL_4(C) an irreducible continuous Galois representation. Let G denote the projective image of ρ in PGL_4(C). We say that ρ is hypertetrahedral if G is an extension of A_4 by the Klein group V_4. In this case, we show that ρ is modular, i.e., ρ corresponds to an automorphic representation π of GL_4(A_F) such that their L-functions are equal. This gives new examples of irreducible 4-dimensional monomial representations which are modular, but are not induced from normal extensions and are not essentially self-dual.

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Additional Information:© 2004 Académie des sciences. Published by Elsevier Masson SAS. Received 15 January 2004, Accepted 11 May 2004, Available online 29 July 2004. The author would like to thank his advisor, Dinakar Ramakrishnan, for suggestions and guidance throughout this work. He is also indebted to the GAP Group as many group and character computations were done in the initial stages of this work using the computer algebra package GAP.
Issue or Number:2
Record Number:CaltechAUTHORS:20170710-105844896
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Official Citation:Kimball Martin, Modularity of hypertetrahedral representations, Comptes Rendus Mathematique, Volume 339, Issue 2, 15 July 2004, Pages 99-102, ISSN 1631-073X, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78891
Deposited By: Ruth Sustaita
Deposited On:10 Jul 2017 18:35
Last Modified:15 Nov 2021 17:43

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