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Grothendieck ring and Verlinde formula for the W-extended logarithmic minimal model WLM(1,p) | | Paul A. Pearce
; Jorgen Rasmussen
; Philippe Ruelle
; | | Date: |
1 Jul 2009 | | Abstract: | 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 formula that is manifestly independent of the
modular parameter $ au$ but is, in fact, equivalent to the Verlinde formula
recently proposed by Gaberdiel and Runkel involving a $ au$-dependent
S-matrix. | | Source: | arXiv, 0907.0134 | | Services: | Forum | Review | PDF | Favorites | |
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