{"paper":{"title":"The minimal monomial lfting of cluster algebras I: branching problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.RT","authors_text":"Luca Francone","submitted_at":"2023-10-18T08:55:43Z","abstract_excerpt":"Let $\\widehat G \\subseteq G$ be complex reductive algebraic groups. The branching problem that aims to study $G$-modules as $\\widehat G$-modules is encoded by a collection of branching multiplicities parameterised by pairs of dominant weights. The branching algebra $Br(G,\\widehat G)$ is a graded algebra whose dimension of homogeneous components are precisely the branching multiplicities. Here, we endow $Br(G, \\widehat G)$ with the structure of a graded upper cluster algebra, for some pair of groups. Our result holds if $\\widehat G$ is a Levi subgroup of $G$ or in the tensor product case, that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.11808","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/2310.11808/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"}