{"paper":{"title":"Permutation actions on modular tensor categories of topological multilayer phases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math.CT","math.MP","math.QA"],"primary_cat":"math-ph","authors_text":"Albert Georg Passegger","submitted_at":"2018-08-20T17:19:18Z","abstract_excerpt":"We find a non-trivial representation of the symmetric group $S_n$ on the $n$-fold Deligne product $\\mathcal{C}^{\\boxtimes n}$ of a modular tensor category $\\mathcal{C}$ for any $n \\geq 2$. This is accomplished by checking that a particular family of $\\mathcal{C}^{\\boxtimes n}$-bimodule categories representing adjacent transpositions satisfies the symmetric group relations with respect to the relative Deligne product. The bimodule categories are based on a permutation action of $S_2$ on $\\mathcal{C}\\boxtimes\\mathcal{C}$ discussed by Fuchs and Schweigert in hep-th/1310.1329 , for which we show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06574","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"}