Abstract
Building on work of the first and last author, we prove that an embedding of simple affine vertex algebras \({V_{\mathbf{k}}({\mathfrak{g}}^0)\subset V_{k}({\mathfrak{g}})}\), corresponding to an embedding of a maximal equal rank reductive subalgebra \({{\mathfrak{g}}^0}\) into a simple Lie algebra \({{\mathfrak{g}}}\), is conformal if and only if the corresponding central charges are equal. We classify the equal rank conformal embeddings. Furthermore we describe, in almost all cases, when \({V_{k}({\mathfrak{g}})}\) decomposes finitely as a \({V_{\mathbf{k}}({\mathfrak{g}}^0)}\)-module.
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Communicated by Y. Kawahigashi
D.A. and O.P. are partially supported by the Croatian Science Foundation under the project 2634 and by the Croatian Scientific Centre of Excellence QuantixLie.
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Adamović, D., Kac, V.G., Möseneder Frajria, P. et al. Finite vs. Infinite Decompositions in Conformal Embeddings. Commun. Math. Phys. 348, 445–473 (2016). https://doi.org/10.1007/s00220-016-2672-1
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DOI: https://doi.org/10.1007/s00220-016-2672-1