{"paper":{"title":"A formula for the $q$-character of functions on the nilpotent cone of some Lie algebra representations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Frank Wang, Vasily Krylov","submitted_at":"2026-08-04T08:21:36Z","abstract_excerpt":"Let $\\mathfrak{g}$ be a reductive Lie algebra and $V$ a finite-dimensional $\\mathfrak{g}$-representation. When $V$ is the representation of a cyclic quiver with equal dimensions, the representation of a cyclic quiver with two vertices, or a representation of a product of copies of $\\mathfrak{sl}_2$ we call an acyclic extended quiver representation of trivial type, we prove a $q$-character formula for the nilpotent cone of $V$ analogous to Hesselink's $q$-character formula of the usual nilpotent cone of $\\mathfrak{g}$. We also define a new class of representations we call Hesselink-type represe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03314","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/2608.03314/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"}