{"paper":{"title":"Rigid Indecomposable Modules in Grassmannian Cluster Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Ana Garcia Elsener, Dusko Bogdanic, Jian-Rong Li, Karin Baur","submitted_at":"2020-11-18T11:56:45Z","abstract_excerpt":"The coordinate ring of the Grassmannian variety of $k$-dimensional subspaces in $\\mathbb{C}^n$ has a cluster algebra structure with Pl\\\"ucker relations giving rise to exchange relations. In this paper, we study indecomposable modules of the corresponding Grassmannian cluster categories ${\\rm CM}(B_{k,n})$. Jensen, King, and Su have associated a Kac-Moody root system $J_{k,n}$ to ${\\rm CM}(B_{k,n})$ and shown that in the finite types, rigid indecomposable modules correspond to roots. In general, the link between the category ${\\rm CM}(B_{k,n})$ and the root system $J_{k,n}$ remains mysterious a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.09227","kind":"arxiv","version":4},"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/2011.09227/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"}