$\ell$-weights and factorization of transfer operators

Abstract

We analyze the $\ell$--weights of the evaluation and $q$-oscillator representations of the quantum loop algebras ${\mathrm{U}}_q(\mathcal{L}({\mathfrak{sl}}_{l+1}))$ for $l=1$ and $l=2$ and prove the factorization relations for the transfer operators of the associated quantum integrable systems.

arXiv comment27 pages, submitted to the proceedings of the International conference "Polivanov-90"

References in corpus (25)

• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Functional Relations in Solvable Lattice Models I: Functional Relations and Representation Theory
• T-systems and Y-systems in integrable systems
• Integrable structure of W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory
• The q-characters of representations of quantum affine algebras and deformations of W-algebras
• Baxter's Relations and Spectra of Quantum Integrable Models
• Baxter's Q-operators for supersymmetric spin chains
• Asymptotic representations and Drinfeld rational fractions
• Convex Bases of PBW type for Quantum Affine Algebras
• Exercises with the universal R-matrix
• The Baxter's Q-operator for the W-algebra $W_N$
• Infinite Families of Gauge-Equivalent $R$-Matrices and Gradations of Quantized Affine Algebras
• Universal R-matrix and functional relations
• Universal integrability objects
• Quantum Affine Algebras and Universal $R$-Matrix with Spectral Parameter
• Oscillator versus prefundamental representations II. Arbitrary higher ranks
• Oscillator versus prefundamental representations
• Quantum groups and functional relations for higher rank
• On the universal R-matrix for the Izergin-Korepin model
• Monodromy operators for higher rank
• Quantum groups, Verma modules and $q$-oscillators: General linear case
• Vertex Models and Spin Chains in Formulas and Pictures
• Reduced qKZ equation: general case

Cited by in corpus (2)

• Quantum groups and functional relations for arbitrary rank
• Khoroshkin-Tolstoy approach for quantum superalgebras