Quantum groups and functional relations for higher rank

Abstract

A detailed construction of the universal integrability objects related to the integrable systems associated with the quantum group ${\mathrm{U}}_q(\mathcal{L}({\mathfrak{sl}}_3))$ is given. The full proof of the functional relations in the form independent of the representation of the quantum group on the quantum space is presented. The case of the general gradation and general twisting is treated. The specialization of the universal functional relations to the case when the quantum space is the state space of a discrete spin chain is described.

LaTeX2e, 47 pages; the version submitted to the Journal of Physics A

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• Complete spectrum of quantum integrable lattice models associated to ${\mathcal{U}}_q(\widehat{g{l}_n})$ by separation of variables
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• On the calculation of the correlation functions of the ${\mathfrak{sl}}_3$-model by means of the reduced qKZ equation
• Quantum groups, Verma modules and $q$-oscillators: General linear case
• An Ising-type formulation of the six-vertex model
• Reduced qKZ equation: general case
• $\ell$-weights and factorization of transfer operators
• Quantum groups and functional relations for arbitrary rank
• Khoroshkin-Tolstoy approach for quantum superalgebras
• Quantum affine algebras and universal functional relations