2009/07/31 by Paul A. Pearce, Paul A Pearce, Jørgen Rasmussen +2
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #cond-mat.stat-mech #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/43/4/045211
published as J.Phys.A43:045211,2010 · 13 pages, v2: example, comments and references added
arxiv created 2009/12/10 · openalex publication_date 2010/01/08 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We consider the Grothendieck ring of the fusion algebra of the W-extended\nlogarithmic minimal model WLM(1,p). Informally, this is the fusion ring of\nW-irreducible characters so it is blind to the Jordan block structures\nassociated with reducible yet indecomposable representations. As in the\nrational models, the Grothendieck ring is described by a simple graph fusion\nalgebra. The 2p-dimensional matrices of the regular representation are mutually\ncommuting but not diagonalizable. They are brought simultaneously to Jordan\nform by the modular data coming from the full (3p-1)-dimensional S-matrix which\nincludes transformations of the p-1 pseudo-characters. The spectral\ndecomposition yields a Verlinde-like formula that is manifestly independent of\nthe modular parameter \τ but is, in fact, equivalent to the Verlinde-like\nformula recently proposed by Gaberdiel and Runkel involving a \τ-dependent\nS-matrix.\n Comment: 13 pages, v2: example, comments and references added