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Conformal embeddings and realizations of certain simple W-algebras Adamovic, Drazen

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We shall first recall explicit realizations of certain affine and superconformal vertex algebras from [D. Adamovic, Transform. Groups (2015)] and study their relations with vertex operator algebras appearing in LCFT. Then we shall consider a generalization motivated by the construction of conformal embeddings of affine vertex algebras in W-algebras. We shall also present a decomposition of a large family of non-rational affine W-algebras as modules for affine vertex operator algebras at admissible and negative levels. A particular emphasis will be put on the application of affine fusion rules and intertwining operators in the determination of branching rules. The second part of this talk is based on a joint paper with V. Kac, P. Moseneder-Frajria, P. Papi and O. Perse.

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