Universal integrability objects

Abstract

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 $U_q(\mathcal{L}({\mathfrak{sl}}_2))$. We give a complete set of the functional relations correcting inexactitudes of the previous considerations. A special attention is given to the connection of the representations used to construct the universal transfer operators and $Q$-operators.

21 pages, submitted to the Proceedings of the International Workshop "CQIS-2012" (Dubna, January 23-27, 2012)

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• A Q-operator for open spin chains I: Baxter's TQ relation
• Vertex Models and Spin Chains in Formulas and Pictures
• Reduced qKZ equation: general case
• Integrable perturbations of conformal field theories and Yetter-Drinfeld modules
• $\ell$-weights and factorization of transfer operators
• Quantum groups and functional relations for arbitrary rank
• On Baxter's Q operator of the higher spin XXZ chain at the Razumov-Stroganov point
• Highest $\ell$-Weight Representations and Functional Relations
• Quantum affine algebras and universal functional relations
• Baxter Q- operator and functional relations