{"paper":{"title":"Zhu's algebra and the $C_2$-algebra in the symplectic and the orthogonal cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG"],"primary_cat":"math.RT","authors_text":"Evgeny Feigin, Peter Littelmann","submitted_at":"2009-11-16T05:55:43Z","abstract_excerpt":"We prove that Zhu's algebra and the $C_2$-algebra of type ${\\tt C}_m$ have the same dimension, and we compute the graded character of the latter. Maximal parabolic subalgebras of the symplectic algebra play a central role in our construction. For the orthogonal algebras our methods do not allow to describe the whole $C_2$-algebras, we get only a description of a certain quotient of the algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2957","kind":"arxiv","version":1},"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"}