{"paper":{"title":"On Cohen-Macaulayness of S_n-invariant subspace arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AC","authors_text":"Aaron Brookner, David Corwin, Pavel Etingof, Steven V Sam","submitted_at":"2014-10-19T17:11:00Z","abstract_excerpt":"Given a partition $\\lambda$ of n, consider the subspace $E_\\lambda$ of $C^n$ where the first $\\lambda_1$ coordinates are equal, the next $\\lambda_2$ coordinates are equal, etc. In this paper, we study subspace arrangements $X_\\lambda$ consisting of the union of translates of $E_\\lambda$ by the symmetric group. In particular, we focus on determining when $X_\\lambda$ is Cohen-Macaulay. This is inspired by previous work of the third author coming from the study of rational Cherednik algebras and which answers the question positively when all parts of $\\lambda$ are equal. We show that $X_\\lambda$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5096","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":""},"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"}