Grothendieck ring and Verlinde-like formula for the {\cal W}-extended logarithmic minimal model {\cal WLM}(1,p)
2010; Institute of Physics; Volume: 43; Issue: 4 Linguagem: Inglês
10.1088/1751-8113/43/4/045211
ISSN1751-8121
AutoresPaul A. Pearce, Jørgen Rasmussen, Philippe Ruelle,
Tópico(s)Advanced Combinatorial Mathematics
ResumoWe 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.
Referência(s)