{"paper":{"title":"Higher order relations for ADE-type generalized q-Onsager algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP","math.QA"],"primary_cat":"math-ph","authors_text":"P. Baseilhac, T.T. Vu","submitted_at":"2013-12-20T11:38:11Z","abstract_excerpt":"Let $\\{A_j|j=0,1,...,rank(g)\\}$ be the fundamental generators of the generalized $q-$Onsager algebra $\\cal O_{q}(\\widehat{g})$ introduced in \\cite{BB1}, where $\\widehat{g}$ is a simply-laced affine Lie algebra. New relations between certain monomials of the fundamental generators - indexed by the integer $r\\in\\mathbb{Z}^{+}$ - are conjectured. These relations can be seen as deformed analogues of Lusztig's $r-$th higher order $q-$Serre relations associated with ${\\cal U}_q({\\widehat g})$, which are recovered as special cases. The relations are proven for $r\\leq 5$. For $r$ generic, several supp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5897","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"}