Indecomposable fusion products |
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| Affiliation: | 1. Division of Biomedical & Life Sciences, Faculty of Health & Medicine, Lancaster University, Lancaster LA1 4YW, UK;2. Department of Management Science, Management School, Lancaster University, Lancaster LA1 4YW, UK;1. Aix Marseille Univ, CNRS, BIP, IMM, Marseille, France;2. Department of Molecular Biosciences, University of Kansas, Lawrence, KS 66045, USA;1. Department of Mathematics, University of Isfahan, Isfahan, P.O. Box 81745-163, Iran;2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran;1. University of Alberta, Canada;2. University of Denver, United States of America;1. School of Mathematics, Georgia Institute of Technology, USA;2. Department of Mathematics, Universität Hamburg, Germany |
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| Abstract: | We analyse the fusion products of certain representations of the Virasoro algebra for c = −2 and c = −7 which are not completely reducible. We introduce a new algorithm which allows us to study the fusion product level by level, and we use this algorithm to analyse the indecomposable components of these fusion products. They form novel representations of the Virasoro algebra which we describe in detail.We also show that a suitably extended set of representations closes under fusion, and indicate how our results generalise to all (1, q) models. |
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