Abstract
Let \(\mathcal {F}_{25}\) be the family of irreducible lowest weight modules for the Virasoro algebra of central charge 25 which are not isomorphic to Verma modules. Let L(25,0) be the Virasoro vertex operator algebra of central charge 25. We prove that the fusion rules for the L(25,0)-modules in \(\mathcal {F}_{25}\) are in correspondence with the tensor rules for the irreducible finite dimensional representations of \(sl(2, \mathbb {C})\), extending the known correspondence between modules for the Virasoro algebras of dual central charges 1 and 25.
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Acknowledgments
The author would like to thank Igor Frenkel for suggesting the study of the case of the Virasoro algebra of central charge 25. The author would also like to thank Igor Frenkel, Jinwei Yang, Antun Milas and Gregg Zuckerman for useful conversations and comments. Finally, the author thanks the reviewer for her/his/their insightful remarks.
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Presented by: Vyjayanthi Chari
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Hunziker, F.O. Fusion Rules for the Virasoro Algebra of Central Charge 25. Algebr Represent Theor 23, 2013–2031 (2020). https://doi.org/10.1007/s10468-019-09923-2
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DOI: https://doi.org/10.1007/s10468-019-09923-2