{"paper":{"title":"Quantum Hamiltonian reduction of W-algebras and category O","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Stephen Morgan","submitted_at":"2015-10-26T02:29:18Z","abstract_excerpt":"We define a quantum version of Hamiltonian reduction by stages, producing a construction in type A for a quantum Hamiltonian reduction from the W-algebra $U(\\mathfrak{g},e_1)$ to an algebra conjecturally isomorphic to $U(\\mathfrak{g},e_2)$, whenever $e_2 \\ge e_1$ in the dominance ordering. This isomorphism is shown to hold whenever $e_1$ is subregular, and in $\\mathfrak{sl}_n$ for all $n \\le 4$.\n  We next define embeddings of various categories $\\mathcal{O}$ for the W-algebras associated to $e_1$ and $e_2$, amongst them the embeddings $\\mathcal{O}(e_2,\\mathfrak{p}) \\hookrightarrow \\mathcal{O}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07352","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"}