摘要翻译：
我们给出了临界渗流的手征融合代数的一个显式猜想，它考虑了没有扩大或扩展对称代数的Virasoro表示。我们用来产生融合的表示形式在数量上是无限的。接下来的融合规则在这样的意义上是准有理的，即有限数目的这些表示的融合分解为这些表示的有限直和。融合规则具有交换性、联想性和sl(2)结构。它们涉及我们称之为Kac表示的表示，其中有些表示是秩1的可约而不可分解的表示。特别地，融合代数的恒等式是秩1的可约但不可分解的Kac表示。我们将我们的融合规则与Eberle-Flohr和Read-Saleur最近的结果进行了详细的比较。值得注意的是，与Eberle-Flohr一致，我们发现秩3的不可分解表示的出现。我们的融合规则得到了一个临界渗流的可积格子模型的大量数值研究的支持。我们的点阵发现和数值结果的细节将在其他地方提出。
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英文标题：
《Fusion algebra of critical percolation》
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作者：
Jorgen Rasmussen and Paul A. Pearce
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：High Energy Physics - Theory        高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Mathematical Physics        数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics        数学
二级分类：Mathematical Physics        数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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英文摘要：
  We present an explicit conjecture for the chiral fusion algebra of critical percolation considering Virasoro representations with no enlarged or extended symmetry algebra. The representations we take to generate fusion are countably infinite in number. The ensuing fusion rules are quasi-rational in the sense that the fusion of a finite number of these representations decomposes into a finite direct sum of these representations. The fusion rules are commutative, associative and exhibit an sl(2) structure. They involve representations which we call Kac representations of which some are reducible yet indecomposable representations of rank 1. In particular, the identity of the fusion algebra is a reducible yet indecomposable Kac representation of rank 1. We make detailed comparisons of our fusion rules with the recent results of Eberle-Flohr and Read-Saleur. Notably, in agreement with Eberle-Flohr, we find the appearance of indecomposable representations of rank 3. Our fusion rules are supported by extensive numerical studies of an integrable lattice model of critical percolation. Details of our lattice findings and numerical results will be presented elsewhere.
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PDF链接：
https://arxiv.org/pdf/706.2716