{"paper":{"title":"Ribbon Hopf algebras from group character rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.RA"],"primary_cat":"math-ph","authors_text":"Bertfried Fauser, Peter D. Jarvis, Ronald C. King","submitted_at":"2012-07-04T19:52:46Z","abstract_excerpt":"We study the diagram alphabet of knot moves associated with the character rings of certain matrix groups. The primary object is the Hopf algebra Char-GL of characters of the finite dimensional polynomial representations of the complex group GL(n) in the inductive limit, realised as the ring of symmetric functions \\Lambda(X) on countably many variables X = {x_1,x_2, ...}. Isomorphic as spaces are the character rings Char-O and Char-Sp of the classical matrix subgroups of GL(n), the orthogonal and symplectic groups. We also analyse the formal character rings Char-H_\\pi\\ of algebraic subgroups of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1094","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"}