WLM（1，p）中的融合矩阵、广义Verlinde公式和配分函数
Fusion matrices, generalized Verlinde formulas, and partition functions in WLM(1,p)
摘要：
在W-扩展图中考虑对数极小模型LM（1，p）的无穷级数，记为WLM（1，p）.在有理模型中，WLM（1，p）的融合代数由一个简单的图融合代数描述。相应的融合矩阵是相互交换的，但一般不能对角化。然而，他们可以同时带来约旦形式的相似性变换。融合矩阵的谱分解是通过一组细化的相似矩阵将融合矩阵转换成由秩为1、2或3的Jordan块组成的Jordan标准形来完成的。从模数据中确定各种相似变换和Jordan形式。这就产生了一个广义Verlinde公式的融合矩阵。在一般框架下讨论了它与模型中的配分函数的关系。通过应用一个特殊的结构矩阵及其Moore-Penrose逆，这个Verlinde公式可化为相应Grothendieck环的广义Verlinde公式.
英文摘要：
The infinite series of logarithmic minimal models LM(1,p) is considered in the W-extended picture where they are denoted by WLM(1,p). As in the rational models, the fusion algebra of WLM(1,p) is described by a simple graph fusion algebra. The corresponding fusion matrices are mutually commuting, but in general not diagonalizable. Nevertheless, they can be simultaneously brought to Jordan form by a similarity transformation. The spectral decomposition of the fusion matrices is completed by a set of refined similarity matrices converting the fusion matrices into Jordan canonical form consisting of Jordan blocks of rank 1, 2 or 3. The various similarity transformations and Jordan forms are determined from the modular data. This gives rise to a generalized Verlinde formula for the fusion matrices. Its relation to the partition functions in the model is discussed in a general framework. By application of a particular structure matrix and its Moore-Penrose inverse, this Verlinde formula reduces to the generalized Verlinde formula for the associated Grothendieck ring.
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