Comptes Rendus
Group Theory/Number Theory
Modularity of hypertetrahedral representations
Comptes Rendus. Mathématique, Volume 339 (2004) no. 2, pp. 99-102.

Let F be a number field, GF its absolute Galois group, and ρ:GFGL4(C) an irreducible continuous Galois representation. Let G¯ denote the projective image of ρ in PGL4(C). We say that ρ is hypertetrahedral if G¯ is an extension of A4 by the Klein group V4. In this case, we show that ρ is modular, i.e., ρ corresponds to an automorphic representation π of GL4(AF) 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.

Soient F un corps de nombres, GF=Gal(F¯/F) et ρ:GFGL4(C) une représentation irréductible et continue. Soit G¯ l'image projective ρ. Nous appellerons une telle représentation hypertétraèdrale si G¯ est une extension de A4 par le groupe de Klein V4. Nous démontrons qu'une représentation hypertétraèdrale est modulaire, i.e., il existe une représentation cuspidale π de GL4(AF) tel que L(s,ρ)=L(s,π). Ceci donne de nouveaux exemples de représentations modulaires qui ne sont pas induites par des extensions normales et ne sont pas essentiellement auto-duales.

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DOI: 10.1016/j.crma.2004.05.003
Kimball Martin 1

1 Caltech 253-37, Pasadena, CA 91125, USA
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Kimball Martin. Modularity of hypertetrahedral representations. Comptes Rendus. Mathématique, Volume 339 (2004) no. 2, pp. 99-102. doi : 10.1016/j.crma.2004.05.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.05.003/

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