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Finite vs. Infinite Decompositions in Conformal Embeddings

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Author(s)
Adamović, Dražen
•
Kac, Victor G
•
Möseneder Frajria, Pierluigi
•
Papi, Paolo
•
Perše, Ozren
Date Issued
2016
Journal
Communications in Mathematical Physics
Publisher
Springer Nature America, Inc
Citation
Adamovic, Drazen, et al. "Finite Vs. Infinite Decompositions in Conformal Embeddings." Communications in Mathematical Physics 348 2 (2016): 445-73.
Version
Author's final manuscript
Abstract
© 2016, Springer-Verlag Berlin Heidelberg. Building on work of the first and last author, we prove that an embedding of simple affine vertex algebras Vk(g0) ⊂ Vk(g) , corresponding to an embedding of a maximal equal rank reductive subalgebra g0 into a simple Lie algebra 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 Vk(g) decomposes finitely as a Vk(g0) -module.
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DOI of Published Version
10.1007/S00220-016-2672-1
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