{"paper":{"title":"Reflective centers of module categories and quantum K-matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Chelsea Walton, Milen Yakimov, Robert Laugwitz","submitted_at":"2023-07-27T10:49:56Z","abstract_excerpt":"Our work is motivated by obtaining solutions to the quantum reflection equation (qRE) by categorical methods. To start, given a braided monoidal category $\\mathcal{C}$ and $\\mathcal{C}$-module category $\\mathcal{M}$, we introduce a version of the Drinfeld center $\\mathcal{Z}(\\mathcal{C})$ of $\\mathcal{C}$ adapted for $\\mathcal{M}$; we refer to this category as the \"reflective center\" $\\mathcal{E}_{\\mathcal{C}}(\\mathcal{M})$ of $\\mathcal{M}$. Just like $\\mathcal{Z}(\\mathcal{C})$ is a canonical braided monoidal category attached to $\\mathcal{C}$, we show that $\\mathcal{E}_{\\mathcal{C}}(\\mathcal{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.14764","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.14764/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}