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 (4)

• A Shortcut to the Q-Operator
• Hidden Grassmann Structure in the XXZ Model II: Creation Operators
• Hidden Grassmann structure in the XXZ model
• Abelian Toda solitons revisited