Grothendieck ring and Verlinde formula for the W-extended logarithmic minimal model WLM(1,p)
(2009) Journal of Physics A: Mathematical and Theoretical — Vol. A43, p. 45211 (2010)
Files
Grothendieckring.pdf
Open Access - Adobe PDF
- 260.44 KB
Details
- Authors
- Abstract
- (en) 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
- Affiliations
Citations
Pearce, P. A., Rasmussen, J., & Ruelle, P. (2009). Grothendieck ring and Verlinde formula for the W-extended logarithmic minimal model WLM(1,p). Journal of Physics A: Mathematical and Theoretical, A43, 45211. https://doi.org/10.1088/1751-8113/43/4/045211 (Original work published 2010)