{"paper":{"title":"A skew Specht perspective of RoCK blocks and cuspidal systems for KLR algebras in affine type A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Liron Speyer, Louise Sutton, Robert Muth, Thomas Nicewicz","submitted_at":"2024-05-24T17:54:40Z","abstract_excerpt":"Cuspidal systems parameterize KLR algebra representations via root partitions $\\pi$, where simple modules $L(\\pi)$ arise as heads of proper standard modules. Working in affine type A with an arbitrary convex preorder, we construct explicit skew diagrams $\\zeta(\\pi)$ such that the skew Specht module $S^{\\zeta(\\pi)}$ has simple head $L(\\pi)$ and a filtration by proper standard modules. A key ingredient in this construction is the development of `core-truncation' functors, which take module categories of level one RoCK blocks to the category of imaginary semicuspidal KLR modules. Every simple ima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.15759","kind":"arxiv","version":3},"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/2405.15759/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"}