Quantum groups and functional relations for arbitrary rank

Abstract

The quantum integrable systems associated with the quantum loop algebras ${\mathrm{U}}_q(\mathcal{L}({\mathfrak{sl}}_{l+1}))$ are considered. The factorized form of the transfer operators related to the infinite dimensional evaluation representations is found and the determinant form of the transfer operators related to the finite dimensional evaluation representations is obtained. The master $TQ$- and $TT$-relations are derived. The operatorial $T$- and $Q$-systems are found. The nested Bethe equations are obtained.

arXiv comment45 pages

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Cited by in corpus (2)

• Transfer matrices of rational spin chains via novel BGG-type resolutions
• Khoroshkin-Tolstoy approach for quantum superalgebras