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arXiv · 1512.03041

Monodromy of the Casimir connection of a symmetrisable Kac-Moody algebra

Andrea Appel·Valerio Toledano-Laredo
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Abstract

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 B_W of W on V. We then prove that this action is canonically equivalent to the quantum Weyl group action of B_W on a quantum deformation of V, that is an integrable, category O-module V_h over the quantum group U_h(g) such that V_h/hV_h is isomorphic to V. This extends a result of the second author which is valid for g semisimple.

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Andrea Appel, Valerio Toledano-Laredo. 2015-12-09. Monodromy of the Casimir connection of a symmetrisable Kac-Moody algebra. https://doi.org/10.1007/s00222-024-01242-8

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