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- W3104037184 abstract "We define the notion of braided Coxeter category, which is informally a tensor category carrying compatible, commuting actions of a generalised braid group B_W and Artin's braid groups B_n on the tensor powers of its objects. The data which defines the action of B_W bears a formal similarity to the associativity constraints in a monoidal category, but is related to the coherence of a family of fiber functors. We show that the quantum Weyl group operators of a quantised Kac-Moody algebra U_h(g), together with the universal R-matrices of its Levi subalgebras, give rise to a braided Coxeter structure on integrable, category O-modules for U_h(g). By relying on the 2-categorical extension of Etingof-Kazhdan quantisation obtained in arXiv:1610.09744, we then prove that this structure can be transferred to integrable, category O-representations of g. These results are used in arXiv:1512.03041 to give a monodromic description of the quantum Weyl group operators of U_h(g) which extends the one obtained by the second author for a semisimple Lie algebra." @default.
- W3104037184 created "2020-11-23" @default.
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- W3104037184 date "2019-07-08" @default.
- W3104037184 modified "2023-10-14" @default.
- W3104037184 title "Coxeter categories and quantum groups" @default.
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- W3104037184 doi "https://doi.org/10.1007/s00029-019-0490-y" @default.
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