{"paper":{"title":"When is a Specht ideal Cohen-Macaulay?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kohji Yanagawa","submitted_at":"2019-02-18T14:06:59Z","abstract_excerpt":"For a partition $\\lambda$ of $n$, let $I^{\\rm Sp}_\\lambda$ be the ideal of $R=K[x_1, \\ldots, x_n]$ generated by all Specht polynomials of shape $\\lambda$. We show that if $R/I^{\\rm Sp}_\\lambda$ is Cohen--Macaulay then $\\lambda$ is of the form either $(a, 1, \\ldots, 1)$, $(a,b)$, or $(a,a,1)$. We also prove that the converse is true if ${\\rm char}(K)=0$. To show the latter statement, the radicalness of these ideals and a result of Etingof et al. are crucial. We also remark that $R/I^{\\rm Sp}_{(n-3,3)}$ is NOT Cohen--Macaulay if and only if ${\\rm char}(K)=2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06577","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":""},"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"}