Caracteres de rigidite du groupe de Grothendieck-Teichmuller

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dc.creatorMarin, Ivan
dc.date2005-02-06
dc.date.accessioned2026-07-07T05:16:44Z
dc.date.available2026-07-07T05:16:44Z
dc.descriptionLet $\k$ be a (topological) field of characteristic 0. Using a Drinfeld associator $Φ$, a representation $Φ(ρ)$ of the braid group over the field $\k((h))$ of Laurent series can be associated to any representation $ρ$ of a certain Hopf algebra $\mathfrak{B}_n(\k)$. We investigate the dependance in $Φ$ of $Φ(ρ)$ for a certain class of representations -- so-called GT-rigid representations -- and deduce from it (continuous) projective representations of the Grothendieck-Teichmuller group $GT_1(\k)$, hence for $\k = \Q_l$ representations of the absolute Galois group of $\Q(μ_{l^{\infty}})$. In most situations, these projective representations can be decomposed into linear characters, which we do for the representations of the Iwahori-Hecke algebra of type A. In this case, we moreover express $Φ(ρ)$ when $Φ$ is even, and get unitary matrix models for the representations of the Iwahori-Hecke algebra. With respect to the action of $GT_1(\k)$, the representations of this algebra corresponding to hook diagrams have noticeable properties.
dc.descriptionFrench; 26 pages
dc.identifierhttps://arxiv.org/abs/math/0502117
dc.identifierhttp://arxiv.org/abs/math/0502117
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74096
dc.subjectRepresentation Theory
dc.subjectNumber Theory
dc.subject14G32, 20C99, 20C08, 20F36
dc.titleCaracteres de rigidite du groupe de Grothendieck-Teichmuller
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