{"paper":{"title":"A classification of commutative parabolic Hecke algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hendrik Van Maldeghem, James Parkinson, Peter Abramenko","submitted_at":"2011-10-27T23:02:22Z","abstract_excerpt":"Let $(W,S)$ be a Coxeter system with $I\\subseteq S$ such that the parabolic subgroup $W_I$ is finite. Associated to this data there is a \\textit{Hecke algebra} $\\scH$ and a \\textit{parabolic Hecke algebra} $\\scH^I=\\mathbf{1}_I\\scH\\mathbf{1}_I$ (over a ring $\\ZZ[q_s]_{s\\in S}$). We give a complete classification of the commutative parabolic Hecke algebras across all Coxeter types."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6214","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"}