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arXiv:0806.3659 · Journal of Statistical Mechanics Theory and Experiment

Reflection matrices for theUq[sl(m|n)(1)] vertex model

A. Lima-Santos

Published Aug 5, 2009• 6 citations
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Abstract

We investigate the possible regular solutions of the boundary Yang–Baxter equation for the vertex models associated with the graded version of the A n −1 (1) affine Lie algebra, the U q [ sl ( m | n ) (1) ] vertex model, also known as the Perk–Schultz model.
DOI
10.1088/1742-5468/2009/08/p08006

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The Perk–Schultz model may be expressed in terms of the solution of the Yang–Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra U q [ gl ( m | n )], with a multiparametric coproduct action as given by Reshetikhin. Here, we present analogous explicit expressions for solutions of the Yang–Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras U q [ osp ( m | n )]. In this manner, we obtain generalizations of the Perk–Schultz model.