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Quasi-Coxeter quasitriangular quasibialgebras and the Casimir connection

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arxiv 1601.04076 v1 pith:QMC3GOC3 submitted 2016-01-15 math.QA math.AGmath.RT

Valerio Toledano-Laredo This is my paper · ORCID
classification math.QAmath.AGmath.RT
keywords casimirconnectionquasi-coxeterquasitriangularalgebragroupquantumquasibialgebra
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Let g be a complex, semisimple Lie algebra. We prove the existence of a quasi-Coxeter, quasitriangular quasibialgebra structure on the enveloping algebra of g, which binds the quasi-Coxeter structure underlying the Casimir connection of g and the quasitriangular quasibialgebra one underlying its KZ equations. This implies in particular that the monodromy of the rational Casimir connection of g is described by the quantum Weyl group operators of the quantum group U_h(g).

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Kohno--Drinfeld Theorem for iquantum Weyl groups

    math.QA 2026-08 conditional novelty 6.0 of 10

    For the split symmetric pair so_m ⊂ sl_m, the monodromy of the boundary Casimir connection is isomorphic to the iota-quantum Weyl group representation.

  2. Quantum Stokes matrices and quantum Riemann-Hilbert-Birkhoff maps

    math-ph 2026-06 unverdicted novelty 6.0 of 10

    Quantum Stokes matrices are constructed for noncommutative meromorphic connections and shown to satisfy exchange relations that realize a deformation quantization of the Riemann-Hilbert-Birkhoff map.

  3. Stokes phenomenon and quantum supergroup $U_q(\mathfrak{gl}(m|n))$

    math.QA 2026-05 unverdicted novelty 5.0 of 10

    Stokes supermatrices of the quantum confluent hypergeometric supersystem for gl(m|n) satisfy the Yang-Baxter equation and give rise to U_q(gl(m|n)).

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