{"paper":{"title":"FI-modules and stability for representations of symmetric groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO","math.GT"],"primary_cat":"math.RT","authors_text":"Benson Farb, Jordan S. Ellenberg, Thomas Church","submitted_at":"2012-04-20T05:25:34Z","abstract_excerpt":"In this paper we introduce and develop the theory of FI-modules. We apply this theory to obtain new theorems about:\n  - the cohomology of the configuration space of n distinct ordered points on an arbitrary (connected, oriented) manifold\n  - the diagonal coinvariant algebra on r sets of n variables\n  - the cohomology and tautological ring of the moduli space of n-pointed curves\n  - the space of polynomials on rank varieties of n x n matrices\n  - the subalgebra of the cohomology of the genus n Torelli group generated by H^1 and more.\n  The symmetric group S_n acts on each of these vector spaces"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4533","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":""},"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"}