{"paper":{"title":"A field-independent filtration of plethystic modules for $\\mathrm{SL}_2(\\mathbb{F})$ that categorifies a product rule for the Cartan subalgebra of $\\mathcal{U}_q(\\mathfrak{sl}_2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"\\'Alvaro Guti\\'errez, \\'Alvaro L. Mart\\'inez, Mark Wildon, Micha{\\l} Szwej","submitted_at":"2026-07-07T19:31:08Z","abstract_excerpt":"We lift a product rule in the Cartan subalgebra of quantum $\\mathfrak{sl}_2$ to a filtration of the plethystic representation $\\Delta^{(n,m)}\\mathrm{Sym}^d E$ of the affine group scheme of the algebraic group $\\mathrm{SL}_2$, where $E$ is the natural representation and $\\Delta^{(n,m)}$ the Weyl functor. This is a significant step towards a categorification of quantum $\\mathfrak{sl}_2$. Our filtration is an addition to a growing family of field-independent isomorphisms of $\\mathrm{SL}_2$ representations that include Hermite reciprocity and the Wronskian isomorphism. It is the first such field-i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06749","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/2607.06749/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"}