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Coxeter categories and quantum groups. (arXiv:1610.09741v3 [math.QA] UPDATED)
来源于:arXiv
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 查看全文>>