{"paper":{"title":"Cyclotomic level maps and associated varieties of simple affine vertex algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.RT","authors_text":"Peng Shan, Qixian Zhao, WenBin Yan","submitted_at":"2025-07-12T11:25:31Z","abstract_excerpt":"In this paper, we introduce and study two cyclotomic level maps defined respectively on the set of nilpotent orbits $\\underline{\\mathcal{N}}$ in a complex semi-simple Lie algebra $\\mathfrak{g}$ and the set of conjugacy classes $\\underline{W}$ in its Weyl group, with values in positive integers. We show that these maps are compatible under Lusztig's map $\\underline{W} \\to \\underline{\\mathcal{N}}$, which is also the minimal reduction type map as shown by Yun. We also discuss their relationship with two-sided cells in affine Weyl groups.\n  We use these maps to formulate a conjecture on the associ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09254","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.09254/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"}