Temperley-Lieb K-matrices

Abstract

This work concerns to the studies of boundary integrability of the vertex models from representations of the Temperley-Lieb algebra associated with the quantum group ${\mathcal{U}}_q[X_n]$ for the affine Lie algebras $X_n$ = $A_1^{(1)}$, $B_n^{(1)}$, $C_n^{(1)}$ and $D_n^{(1)}$. A systematic computation method is used to constructed solutions of the boundary Yang-Baxter equations. We find a $2n^2+1$ free parameter solution for $A_1^{(1)}$ spin-$(n-1/2)$ and $C_n^{(1)}$ vertex models. It turns that for $A_1^{(1)}$ spin-$n$, $B_n^{(1)}$ and $D_n^{(1)}$ vertex models, the solution has $2n^2+2n+1$ free parameters.

arXiv comment20 pages. Improved version with enlarged reference list. arXiv admin note: substantial text overlap with arXiv:1011.2891