{"paper":{"title":"Conformal embeddings of affine vertex algebras in minimal $W$-algebras II: decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.RT","authors_text":"Drazen Adamovic, Ozren Perse, Paolo Papi, Pierluigi Moseneder Frajria, Victor G. Kac","submitted_at":"2016-04-04T15:02:46Z","abstract_excerpt":"We present methods for computing the explicit decomposition of the minimal simple affine $W$-algebra $W_k(\\mathfrak g, \\theta)$ at a conformal level $k$ as a module for its maximal affine subalgebra $\\mathcal V_k(\\mathfrak g^{\\natural})$. A particular emphasis is given on the application of affine fusion rules to the determination of branching rules. In almost all cases when $\\mathfrak g^{\\natural}$ is a semisimple Lie algebra, we show that, for a suitable conformal level $k$, $W_k(\\mathfrak g, \\theta)$ is isomorphic to an extension of $\\mathcal V_k(\\mathfrak g^{\\natural})$ by its simple modul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00893","kind":"arxiv","version":3},"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"}