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Universal integrability objects. (English. Russian original) Zbl 1280.81068
Theor. Math. Phys. 174, No. 1, 21-39 (2013); translation from Teor. Mat. Fiz. 174, No. 1, 25-45 (2013).
Summary: We discuss the main points of the quantum group approach in the theory of quantum integrable systems and illustrate them for the case of the quantum group \(\mathrm{U}_q(\mathcal L(\mathfrak{sl}_2))\). We give a complete set of the functional relations correcting inexactitudes in the previous considerations. We especially attend to the interrelation of the representations used to construct the universal transfer operators and \(Q\)-operators.

MSC:
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81R12 Groups and algebras in quantum theory and relations with integrable systems
17B37 Quantum groups (quantized enveloping algebras) and related deformations
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