{"paper":{"title":"Systems of correlation functions, coinvariants and the Verlinde algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.AG","math.MP"],"primary_cat":"math.RT","authors_text":"Evgeny Feigin","submitted_at":"2010-03-15T16:11:11Z","abstract_excerpt":"We study the Gaberdiel-Goddard spaces of systems of correlation functions attached to an affine Kac-Moody Lie algebra $\\gh$. We prove that these spaces are isomorphic to the spaces of coinvariants with respect to certain subalgebras of $\\gh$. This allows to describe the Gaberdiel-Goddard spaces as direct sums of tensor products of irreducible $\\g$-modules with multiplicities given by fusion coefficients. We thus reprove and generalize Frenkel-Zhu's theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2949","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"}