{"paper":{"title":"The Hopf Algebra Structure of the Character Rings of Classical Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RA"],"primary_cat":"math.RT","authors_text":"Bertfried Fauser, Peter D. Jarvis, Ronald C. King","submitted_at":"2007-04-16T16:22:05Z","abstract_excerpt":"The character ring \\CGL of covariant irreducible tensor representations of the general linear group admits a Hopf algebra structure isomorphic to the Hopf algebra \\Sym$ of symmetric functions. Here we study the character rings \\CO and \\CSp of the orthogonal and symplectic subgroups of the general linear group within the same framework of symmetric functions. We show that \\CO and \\CSp also admit natural Hopf algebra structures that are isomorphic to that of \\CGL, and hence to \\Sym. The isomorphisms are determined explicitly, along with the specification of standard bases for \\CO and \\CSp analog"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.2029","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"}