{"id":426,"date":"2016-10-25T13:10:23","date_gmt":"2016-10-25T11:10:23","guid":{"rendered":"http:\/\/bela.phy.hr\/quantixlie\/?p=426"},"modified":"2016-10-25T16:12:25","modified_gmt":"2016-10-25T14:12:25","slug":"finite-vs-infinite-decompositions-in-conformal-embeddings","status":"publish","type":"post","link":"http:\/\/bela.phy.hr\/quantixlie\/finite-vs-infinite-decompositions-in-conformal-embeddings\/","title":{"rendered":"Finite vs. Infinite Decompositions in Conformal Embeddings"},"content":{"rendered":"

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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}\" \u00a0into 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.<\/span><\/p>\n

Communicated by Y. Kawahigashi.\u00a0D.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.<\/p>\n

Dra\u017een\u00a0Adamovi\u0107,\u00a0<\/span>Victor\u00a0G.\u00a0Kac,\u00a0Pierluigi\u00a0M\u00f6seneder Frajria,\u00a0Paolo\u00a0Papi,\u00a0Ozren\u00a0Per\u0161e,\u00a0Finite vs. Infinite Decompositions in Conformal Embeddings<\/a>,\u00a0Communications in Mathematical Physics<\/a>,\u00a0<\/span>Issue\u00a02<\/a>, pp 445\u2013473.\u00a0doi:10.1007\/s00220-016-2672-1.<\/span><\/p>\n

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