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Creators/Authors contains: "Toledano Laredo, Valerio"

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  1. ; (, Inventiones mathematicae)
    Let g be a symmetrisable Kac-Moody algebra and V an integrable g-module in category O. We show that the monodromy of the (normally ordered) rational Casimir connection on V can be made equivariant with respect to the Weyl group W of g, and therefore defines an action of the braid group BW on V. We then prove that this action is canonically equivalent to the quantum Weyl group action of BW on a quantum deformation of V, that is an integrable, category O module V over the quantum group Uhg such that V/hV is isomorphic to V. This extends a result of the second author which is valid for g semisimple. 
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  2. ; (, Pure and Applied Mathematics Quarterly)
    Let be a symmetrisable Kac–Moody algebra and Uhg its quantised enveloping algebra. Answering a question of P. Etingof, we prove that the quantum Weyl group operators of Uhg give rise to a canonical action of the pure braid group of g on any category O (not necessarily integrable) module. By relying on our recent results, we show that this action describes the monodromy of the rational Casimir connection on the Uhg-module corresponding to V. We also extend these results to yield equivalent representations of parabolic pure braid groups on parabolic category for Uhg and g. 
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  3. ; (, Advances in Mathematics)
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