{"paper":{"title":"Multiplicative Bases for the Centres of the Group Algebra and Iwahori-Hecke Algebra of the Symmetric Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Andrew Francis, Lenny Jones","submitted_at":"2012-05-30T21:21:20Z","abstract_excerpt":"Let $\\H_n$ be the Iwahori-Hecke algebra of the symmetric group $S_n$, and let $Z(\\H_n)$ denote its centre. Let $B={b_1,b_2,...,b_t}$ be a basis for $Z(\\H_n)$ over $R=\\Z[q,q^{-1}]$. Then $B$ is called \\emph{multiplicative} if, for every $i$ and $j$, there exists $k$ such that $b_ib_j= b_k$. In this article we prove that there are no multiplicative bases for $Z(\\Z S_n)$ and $Z(\\H_n)$ when $n\\ge 3$. In addition, we prove that there exist exactly two multiplicative bases for $Z(\\Z S_2)$ and none for $Z(\\H_2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6837","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"}