Un théorème de Kohno-Drinfeld pour les connexions de Knizhnik-Zamolodchikov cyclotomiques

Abstract : In this thesis, we give an explicit computation of the monodromy representations of "cyclotomic" analogs of the Knizhnik--Zamolodchikov differential system. These are representations of the type B braid group $B_n^1$. We show how the representations of the braid group $B_n$ obtained using quantum groups and universal $R$-matrices may be enhanced to representations of $B_n^1$ using dynamical twists. Then, we show how these "algebraic" representations may be identified with the above "analytic" monodromy representations.
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Adrien Brochier. Un théorème de Kohno-Drinfeld pour les connexions de Knizhnik-Zamolodchikov cyclotomiques. Mathématiques [math]. Université de Strasbourg, 2011. Français. ⟨NNT : 2011STRA6168⟩. ⟨tel-00598766⟩

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