Pearce, Paul A.
Rasmussen, Jorgen
Ruelle, Philippe
[UCL]
(eng)
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 $\tau$ but is, in fact, equivalent to the Verlinde-like
formula recently proposed by Gaberdiel and Runkel involving a $\tau$-dependent
S-matrix.
Comment: 13 pages, v2: example, comments and references added
Bibliographic reference |
Pearce, Paul A. ; Rasmussen, Jorgen ; Ruelle, Philippe. Grothendieck ring and Verlinde formula for the W-extended logarithmic minimal model WLM(1,p). In: Journal of Physics A: Mathematical and Theoretical, Vol. A43, p. 045211 (2010) |
Permanent URL |
http://hdl.handle.net/2078/31233 |