On the universal R-matrix for the Izergin-Korepin model

Abstract

We continue our exercises with the universal $R$-matrix based on the Khoroshkin and Tolstoy formula. Here we present our results for the case of the twisted affine Kac--Moody Lie algebra of type $A_2^{(2)}$. Our interest in this case is inspired by the fact that the Tzitzéica equation is associated with $A_2^{(2)}$ in a similar way as the sine-Gordon equation is related to $A_1^{(1)}$. The fundamental spin-chain Hamiltonian is constructed systematically as the logarithmic derivative of the transfer matrix. $L$-operators of two types are obtained by using q-deformed oscillators.

26 pages; comments and refs added, version to appear in J. Phys. A: Math. Theor

References in corpus (9)

• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• A Shortcut to the Q-Operator
• Integrable structure of W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory
• Hidden Grassmann Structure in the XXZ Model II: Creation Operators
• Hidden Grassmann structure in the XXZ model
• Analytical Bethe Ansatz for Quantum-Algebra-Invariant Spin Chains
• Exercises with the universal R-matrix
• Infinite Families of Gauge-Equivalent $R$-Matrices and Gradations of Quantized Affine Algebras
• Abelian Toda solitons revisited

Cited by in corpus (13)

• Universal R-matrix and functional relations
• Construction of $R$-matrices for symmetric tensor representations related to $U_q(\widehat{s{l}_n})$
• Universal integrability objects
• Oscillator versus prefundamental representations
• Quantum groups and functional relations for higher rank
• The universal R-matrix and factorization of the L-operators related to the Baxter Q-operators
• Monodromy operators for higher rank
• Vertex Models and Spin Chains in Formulas and Pictures
• Reduced qKZ equation: general case
• Quantum groups and functional relations for arbitrary rank
• $\ell$-weights and factorization of transfer operators
• Khoroshkin-Tolstoy approach for quantum superalgebras
• Quantum affine algebras and universal functional relations