{"paper":{"title":"Cluster Algebras for Bosonic Plethysm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CO"],"primary_cat":"math.RT","authors_text":"Jiarui Fei, Yelin Fan","submitted_at":"2026-08-02T03:22:24Z","abstract_excerpt":"Let $\\Bbbk$ be an algebraically closed field of characteristic zero, let $V=\\Bbbk^\\ell$ and $W=\\Bbbk^m$, and set \\[ \\mathcal R_{\\ell,m}=\\operatorname{Sym}(\\operatorname{Sym}^2V\\otimes W)^{U_V}. \\] We construct an explicit skew-symmetrizable seed $\\Sigma_{\\ell,m}$ by restricting and folding the determinantal seed for the flagged $m$-arrow Kronecker quiver. For every $\\ell,m\\ge2$, we have \\[ \\mathcal R_{\\ell,m}=\\mathcal U(\\Sigma_{\\ell,m}), \\] with polynomial frozen coefficients, and $\\Sigma_{\\ell,m}$ admits a reddening sequence. The theta basis extends across the frozen boundary exactly for para"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00963","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.00963/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"}