{"paper":{"title":"On purity theorem of Lusztig's perverse sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.QA"],"primary_cat":"math.RT","authors_text":"Fan Xu, Jie Xiao, Minghui Zhao","submitted_at":"2017-12-12T08:24:01Z","abstract_excerpt":"Let $Q$ be a finite quiver without loops and $\\mathcal{Q}_{\\alpha}$ be the Lusztig category for any dimension vector $\\alpha$. The purpose of this paper is to prove that all Frobenius eigenvalues of the $i$-th cohomology $\\mathcal{H}^i(\\mathcal{L})|_x$ for a simple perverse sheaf $\\mathcal{L}\\in \\mathcal{Q}_{\\alpha}$ and $x\\in \\mathbb{E}_{\\alpha}^{F^n}=\\mathbb{E}_{\\alpha}(\\mathbb{F}_{q^n})$ are equal to $(\\sqrt{q^n})^{i}$ as a conjecture given by Schiffmann (\\cite{Schiffmann2}). As an application, we prove the existence of a class of Hall polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04167","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":""},"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"}