A Bijection Between Paths for the M(p, 2p + 1){mathcal{M}(p, 2p + 1)} Minimal Model Virasoro Characters

Olivier Blondeau-Fournier; Pierre Mathieu; Trevor A. Welsh

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A Bijection Between Paths for the M(p, 2p + 1){mathcal{M}(p, 2p + 1)} Minimal Model Virasoro Characters

机译：M（p，2p +1）{mathcal {M}（p，2p +1）}最小模型维拉索罗字符在路径之间的双射

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The states in the irreducible modules of the minimal models can be represented by infinite lattice paths arising from consideration of the corresponding RSOS statistical models. For the models, a completely different path representation has been found recently, this one on a half-integer lattice; it has no known underlying statistical-model interpretation. The correctness of this alternative representation has not yet been demonstrated, even at the level of the generating functions, since the resulting fermionic characters differ from the known ones. This gap is filled here, with the presentation of two versions of a bijection between the two path representations of the states. In addition, a half-lattice path representation for the models is stated, and other generalisations suggested.

机译：最小模型的不可约模块中的状态可以由考虑相应的RSOS统计模型而产生的无限晶格路径表示。对于这些模型，最近发现了一种完全不同的路径表示形式，该路径表示形式是半整数格。它没有已知的基础统计模型解释。甚至在产生功能的水平上，这种替代表示的正确性尚未得到证明，因为所得的铁离子特征不同于已知的。在这里，通过状态的两个路径表示之间的双射的两个版本的表示填补了这一空白。此外，陈述了模型的半晶格路径表示，并提出了其他概括。

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《Annales Henri Poincare》 |2010年第2期|p.101-125|共25页
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Olivier Blondeau-Fournier; Pierre Mathieu; Trevor A. Welsh;
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1. A bijection between paths for the M(p, 2p + 1) minimal model virasoro characters [J] . Blondeau-Fournier O., Mathieu P., Welsh T.A. Annales Henri Poincare . 2010,第1a2期

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A Bijection Between Paths for the M(p, 2p + 1){mathcal{M}(p, 2p + 1)} Minimal Model Virasoro Characters

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