Abstract
The infinite series of logarithmic minimal models is considered in the -extended picture where they are denoted by . As in the rational models, the fusion algebra of 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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