{"paper":{"title":"Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alistair Savage, Marco Mackaay","submitted_at":"2017-05-08T20:01:23Z","abstract_excerpt":"We associate a monoidal category $\\mathcal{H}^\\lambda$ to each dominant integral weight $\\lambda$ of $\\widehat{\\mathfrak{sl}}_p$ or $\\mathfrak{sl}_\\infty$. These categories, defined in terms of planar diagrams, act naturally on categories of modules for the degenerate cyclotomic Hecke algebras associated to $\\lambda$. We show that, in the $\\mathfrak{sl}_\\infty$ case, the level $d$ Heisenberg algebra embeds into the Grothendieck ring of $\\mathcal{H}^\\lambda$, where $d$ is the level of $\\lambda$. The categories $\\mathcal{H}^\\lambda$ can be viewed as a graphical calculus describing induction and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03066","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"}