{"paper":{"title":"Theta functions for lattices of SU(3) hyper-roots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Robert Coquereaux","submitted_at":"2017-08-02T00:32:02Z","abstract_excerpt":"We recall the definition of the hyper-roots that can be associated to modules-categories over the fusion categories defined by the choice of a simple Lie group G together with a positive integer k. This definition was proposed in 2000, using another language, by Adrian Ocneanu. If G=SU(2), the obtained hyper-roots coincide with the usual roots for ADE Dynkin diagrams. We consider the associated lattices when G=SU(3) and determine their theta functions in a number of cases; these functions can be expressed as modular forms twisted by appropriate Dirichlet characters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00560","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"}