{"paper":{"title":"Free wreath product quantum groups : the monoidal category, approximation properties and free probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Fran\\c{c}ois Lemeux, Pierre Tarrago","submitted_at":"2014-11-15T08:50:52Z","abstract_excerpt":"In this paper, we find the fusion rules for the free wreath product quantum groups $\\mathbb{G}\\wr_*S_N^+$ for all compact matrix quantum groups of Kac type $\\mathbb{G}$ and $N\\ge4$. This is based on a combinatorial description of the intertwiner spaces between certain generating representations of $\\mathbb{G}\\wr_*S_N^+$. The combinatorial properties of the intertwiner spaces in $\\mathbb{G}\\wr_*S_N^+$ then allows us to obtain several probabilistic applications. We then prove the monoidal equivalence between $\\mathbb{G}\\wr_*S_N^+$ and a compact quantum group whose dual is a discrete quantum subg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4124","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"}