A Kohno-Drinfeld theorem for quantum Weyl groups

DOI10.1215/S0012-9074-02-11232-0zbMath1016.17010arXivmath/0009181OpenAlexW2011929815MaRDI QIDQ1847918

Valerio Toledano Laredo

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0009181

zbMATH Keywords

monodromyquantum groupsconnectionsgeneralised braid groupsquantum Weyl group action

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Braid groups; Artin groups (20F36) Monodromy; relations with differential equations and (D)-modules (complex-analytic aspects) (32S40) Ring-theoretic aspects of quantum groups (16T20)

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Cites Work

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• The symplectic geometry of polygons in Euclidean space
• q-Weyl group and a multiplicative formula for universal R-matrices
• Some applications of the quantum Weyl groups
• An analogue of P.B.W. theorem and the universal R-matrix for \(U_ h\mathfrak{sl}(N+1)\)
• On quantum groups
• The Gelfand-Cetlin system and quantization of the complex flag manifolds
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Structure of quasitriangular quasi-Hopf algebras
• Finite-dimensional representations of quantum affine algebras
• A Littelmann-type formula for Duistermaat-Heckman measures
• PBW basis of quantized universal enveloping algebras
• Polygon spaces and Grassmannians
• Differential equations compatible with KZ equations
• Integrable connections related to Manin and Schechtman's higher braid groups
• Casimir operators and monodromy representations of generalised braid groups
• Normalisateurs de tores. I: Groupes de Coxeter etendus
• Die Fundamentalgruppe des Raumes der regulären Orbits einer endlichen komplexen Spiegelungsgruppe
• Finite Dimensional Hopf Algebras Arising From Quantized Universal Enveloping Algebras
• Remarks on Classical Invariant Theory
• Quantum linear groups
• Introduction to quantum groups