边界环模型的组合问题
Combinatorial aspects of boundary loop models
摘要：
我们在本文中讨论组合方面的边界循环模型，即模型的自避免循环上的一条循环得到不同的权重取决于他们是否接触的左，右，两者或没有边界。这些模型的代数描述的Temperley-Lieb代数的推广，被称为双边界TL代数。我们给出了TL表示的维数和相应的退化的配分函数的结果。我们解释这些结果的融合和最近发现的A_n大对称性存在于环路模型，铺平了道路的分析共形场论的性质。最后，我们提出了在所有情况下，包括两个边界的一个，这是最近讨论的de Gier和Nichols的格拉姆矩阵的行列式的图解。
英文摘要：
We discuss in this paper combinatorial aspects of boundary loop models, that is models of self-avoiding loops on a strip where loops get different weights depending on whether they touch the left, the right, both or no boundary. These models are described algebraically by a generalization of the Temperley-Lieb algebra, dubbed the two-boundary TL algebra. We give results for the dimensions of TL representations and the corresponding degeneracies in the partition functions. We interpret these results in terms of fusion and in the light of the recently uncovered A_n large symmetry present in loop models, paving the way for the analysis of the conformal field theory properties. Finally, we propose conjectures for determinants of Gram matrices in all cases, including the two-boundary one, which has recently been discussed by de Gier and Nichols.
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