{"paper":{"title":"Gr\\\"obner-Shirshov bases for Temperley-Lieb algebras of the complex reflection group of type $G(d,1,n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Dong-il Lee, Jeong-Yup Lee, Sungsoon Kim","submitted_at":"2018-08-17T05:12:16Z","abstract_excerpt":"We construct a Gr\\\"obner-Shirshov basis of the Temperley-Lieb algebra $\\mathfrak{T}(d,n)$ of the complex reflection group $G(d,1,n)$, inducing the standard monomials expressed by the generators $\\{E_i\\}$ of $\\mathfrak{T}(d,n)$. This result generalizes the one for the Coxeter group of type $B_n$ in \\cite{KimSSLeeDI}. We also give a combinatorial interpretation of the standard monomials of $\\mathfrak{T}(d,n)$, relating to the fully commutative elements of the complex reflection group $G(d,1,n)$. In this way, we obtain the dimension formula of $\\mathfrak{T}(d,n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06523","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"}