arXiv:1101.0540

Temperley-Lieb K-matrices

A. Lima-Santos

Published Jan 3, 2011• 0 citations

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 ${\cal U}_{q}[X_{n}]$ 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.

DOI: 10.48550/arxiv.1101.0540

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arXiv:1101.0540

Temperley-Lieb K-matrices

A. Lima-Santos

Published Jan 3, 2011• 0 citations

arXiv HTML PDF

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

{\cal 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.

DOI: 10.48550/arxiv.1101.0540

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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

{\cal 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.

On the multiparametric

{\mathcal{U}}_{q}[{D}_{n+1}^{(2)}]

vertex model