Représentations linéaires des tresses infinitésimales

Abstract : This work contributes to the general study of linear representations of Artin's Braid group $B_n$ that arise as monodromy of KZ-systems. We consider these systems as representations of the Hopf algebra of infinitesimal braids, and apply the technique of Gelfand-Tsetlin basis. The purpose is twofold : this technique gives a good insight into the representation theory of this algebra, and we show that it helps in the explicit construction of the corresponding braid group representations. We give a complete classification of KZ-systems that are irreducible for the action of the symmetric group, and build the new representations of $B_n$ that arise at this stage. Among other results that are useful in this setting, we obtain irreducibility criteria on tensor products and related constructions, and get a partial decomposition of the Lie algebra generated by transpositions in the group algebra of the symmetric group. This partial decomposition involves summands of the Jones representation.
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https://tel.archives-ouvertes.fr/tel-00005386
Contributor : Ivan Marin <>
Submitted on : Thursday, March 18, 2004 - 7:02:39 PM
Last modification on : Tuesday, September 22, 2020 - 3:52:47 AM
Long-term archiving on: : Wednesday, September 12, 2012 - 2:15:09 PM

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• HAL Id : tel-00005386, version 1

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Ivan Marin. Représentations linéaires des tresses infinitésimales. Mathématiques [math]. Université Paris Sud - Paris XI, 2001. Français. ⟨tel-00005386⟩

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