W-扩展对数极小模型WLM（1，p）的Grothendieck环和Verlinder型公式
Grothendieck ring and Verlinde-like formula for the W-extended logarithmic minimal model WLM(1,p)
摘要：
考虑W-扩张对数极小模型WLM（1，p）的融合代数的Grothendieck环.非正式地，这是W-不可约特征标的融合环，因此它对与可约但不可分解表示相关联的Jordan块结构是盲目的。在有理模型中，Grothendieck环由一个简单的图融合代数描述。正则表示的2 p维矩阵是可交换的，但不可对角化。它们通过来自全（3 p-1）维S-矩阵的模数据同时被带到Jordan形式，该S-矩阵包括p-1伪特征标的变换。的谱分解产生一个Verlinde的公式，显然是独立的模块参数$τ$，但事实上，相当于最近提出的Verlinde的公式由Gaberdiel和Runkel涉及$τ$依赖的S-矩阵。
英文摘要：
We consider the Grothendieck ring of the fusion algebra of the W-extended logarithmic minimal model WLM(1,p). Informally, this is the fusion ring of W-irreducible characters so it is blind to the Jordan block structures associated with reducible yet indecomposable representations. As in the rational models, the Grothendieck ring is described by a simple graph fusion algebra. The 2p-dimensional matrices of the regular representation are mutually commuting but not diagonalizable. They are brought simultaneously to Jordan form by the modular data coming from the full (3p-1)-dimensional S-matrix which includes transformations of the p-1 pseudo-characters. The spectral decomposition yields a Verlinde-like formula that is manifestly independent of the modular parameter $τ$ but is, in fact, equivalent to the Verlinde-like formula recently proposed by Gaberdiel and Runkel involving a $τ$-dependent S-matrix.
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