{"paper":{"title":"Elementary construction of the minimal free resolution of the Specht ideal of shape $(n-d,d)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AC","authors_text":"Kohji Yanagawa, Kosuke Shibata","submitted_at":"2022-06-06T15:59:46Z","abstract_excerpt":"Let $K$ be a field with ${\\rm char}(K)=0$. For a partition $\\lambda$ of $n \\in {\\mathbb N}$, let $I^{\\rm Sp}_\\lambda$ be the ideal of $R=K[x_1,\\ldots,x_n]$ generated by all Specht polynomials of shape $\\lambda$. These ideals have been studied from several points of view (and under several names). Using advanced tools of the representation theory, Berkesch Zamaere et al [BGS]. constructed a minimal free resolution of $I^{\\rm Sp}_{(n-d,d)}$ except differential maps. The present paper constructs the differential maps, and also gives an elementary proof of the result of [BGS]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.02701","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/2206.02701/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"}