{"paper":{"title":"Symmetric modules over the infinite polynomial ring I: nilpotent quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AC","authors_text":"Andrew Snowden, Rohit Nagpal, Teresa Yu","submitted_at":"2025-08-06T16:51:07Z","abstract_excerpt":"Cohen proved that the infinite variable polynomial ring $R=k[x_1,x_2,\\ldots]$ is noetherian with respect to the action of the infinite symmetric group $\\mathfrak{S}$. The first two authors began a program to understand the $\\mathfrak{S}$-equivariant algebra of $R$ in detail. In previous work, they classified the $\\mathfrak{S}$-prime ideals of $R$. An important example of an $\\mathfrak{S}$-prime is the ideal $\\mathfrak{h}_s$ generated by $(s+1)$st powers of the variables. In this paper, we study the category of $R/\\mathfrak{h}_s$-modules. We obtain a number of results, and mention just three he"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.04624","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.04624/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"}