{"paper":{"title":"On the structure of cyclotomic nilHecke algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jun Hu, Xinfeng Liang","submitted_at":"2017-09-26T00:22:38Z","abstract_excerpt":"In this paper we study the structure of the cyclotomic nilHecke algebras $\\HH_{\\ell,n}^{(0)}$, where $\\ell,n\\in\\N$. We construct a monomial basis for $\\HH_{\\ell,n}^{(0)}$ which verifies a conjecture of Mathas. We show that the graded basic algebra of $\\HH_{\\ell,n}^{(0)}$ is commutative and hence isomorphic to the center $Z$ of $\\HH_{\\ell,n}^{(0)}$. We further prove that $\\HH_{\\ell,n}^{(0)}$ is isomorphic to the full matrix algebra over $Z$ and construct an explicit basis for the center $Z$. We also construct a complete set of pairwise orthogonal primitive idempotents of $\\HH_{\\ell,n}^{(0)}$. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08760","kind":"arxiv","version":4},"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"}