{"paper":{"title":"Finite vs infinite decompositions in conformal embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Drazen Adamovic, Ozren Perse, Paolo Papi, Pierluigi Moseneder Frajria, Victor G. Kac","submitted_at":"2015-09-22T09:00:54Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06512","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}