1995/10/24 by V. B. Petkova, Jean-Bernard Zuber, J. -B. Zuber · 1 citation
Mathematics · Physics and Astronomy · #Adjacency matrix #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Combinatorics #Conformal field theory #Conformal map #Discrete mathematics #Eigenvalues and eigenvectors #Geometry #Graph #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Operator algebra #Operator product expansion #Physics #Pure mathematics #Quantum mechanics #Structure constants #hep-th
paper · pdf · doi:10.1016/0550-3213(95)00670-2
published as Nucl.Phys. B463 (1996) 161-193 · 44 pages, 6 postscript figures, the whole uuencoded. TEX file, macros used : harvmac.tex , epsf.tex. Optionally, AMS fonts in amssym.def and amssym.tex
arxiv created 1995/10/24 · openalex publication_date 1996/03/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper, we pursue the discussion of the connections between rational conformal field theories (CFT) and graphs. We generalize our recent work on the relations of operator product algebra (OPA) structure constants of sl(2) theories with the Pasquier algebra attached to the graph. We show that in a variety of CFT built on sl(n) -- typically conformal embeddings and orbifolds, similar considerations enable one to write a linear system satisfied by the matrix elements of the Pasquier algebra in terms of conformal data -- quantum dimensions and fusion coefficients. In some cases, this provides a sufficient information for the determination of all the eigenvectors of an adjacency matrix, and hence of a graph.