标题： 半格路径和Virasoro特征 显示英文标题

标题： Half-lattice paths and Virasoro characters

摘要： 我们首先简要回顾格点路径在导出Virasoro李代数的M(p,p')最小模型特征函数的费米子表达式中的作用。 我们随后关注最近引入的M(p,2p+/-1)特征函数的半格点路径，以一种方式重新表述它们，使得两种情况可以统一处理。 通过描述这些半格点路径与相应RSOS格点路径之间的权重保持双射，证明了这些半格点路径的生成函数确实是M(p,2p+/-1)特征函数。 在此，首次推导了M(p,2p-1)的情况。 然后，我们将Bressoud和Warnaar的方法应用于这些半格点路径，以导出与从RSOS路径获得的不同的Virasoro特征函数X^{p,2p±1}_{1,2}的费米子表达式。 这项工作是对第三作者在“第七届格点路径组合学与应用国际会议”上所展示工作的扩展，该会议于2010年7月在意大利西耶纳举行。 显示英文摘要

摘要： We first briefly review the role of lattice paths in the derivation of fermionic expressions for the M(p,p') minimal model characters of the Virasoro Lie algebra. We then focus on the recently introduced half-lattice paths for the M(p,2p+/-1) characters, reformulating them in such a way that the two cases may be treated uniformly. That the generating functions of these half-lattice paths are indeed M(p,2p+/-1) characters is proved by describing weight preserving bijections between them and the corresponding RSOS lattice paths. Here, the M(p,2p-1) case is derived for the first time. We then apply the methods of Bressoud and Warnaar to these half-lattice paths to derive fermionic expressions for the Virasoro characters X^{p,2p+/-1}_{1,2} that differ from those obtained from the RSOS paths. This work is an extension of that presented by the third author at the "7th International Conference on Lattice Path Combinatorics and Applications", Siena, Italy, July 2010.