Fusion algebras for \(N=1\) superconformal field theories through coinvariants. I: \(\widehat{osp}(1|2)\)-symmetry (Q2703576)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fusion algebras for \(N=1\) superconformal field theories through coinvariants. I: \(\widehat{osp}(1|2)\)-symmetry |
scientific article |
Statements
7 March 2001
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fusion rules
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WZNW models
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Kac-Moody algebras
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superalgebras
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0.9728863
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0.95335704
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0.88268363
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0.8777845
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0.8732509
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0.8731975
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0.8731687
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0.87208855
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Fusion algebras for \(N=1\) superconformal field theories through coinvariants. I: \(\widehat{osp}(1|2)\)-symmetry (English)
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Fusion algebras of the super Wess-Zumino-Novikov-Witten model with \(\widehat{osp}(1|2)\)-symmetry are computed through the computation of the cohomologies of nilpotent subalgebras. First the definition of contragredient Lie superalgebras is given and the Shapovalov determinant formulae for a symmetrizable contragredient Lie superalgebra is stated. As an application the character sum formula for the Jantzen filtration on Verma modules is obtained. Kac-Moody superalgebras are introduced. A Bernstein-Gel'fand-Gel'fand (BGG) resolution for symmetrizable Kac-Moody superalgebras of rank 2 is constructed. Finally, as an application, the above mentioned fusion algebras are computed.
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