{"paper":{"title":"On inductive construction of Procesi bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Ivan Losev","submitted_at":"2019-01-17T16:07:39Z","abstract_excerpt":"A Procesi bundle, a rank $n!$ vector bundle on the Hilbert scheme $H_n$ of $n$ points in $\\mathbb{C}^2$, was first constructed by Mark Haiman in his proof of the $n!$ theorem by using a complicated combinatorial argument. Since then alternative constructions of this bundle were given by Bezrukavnikov-Kaledin and by Ginzburg. In this paper we give a geometric/ representation-theoretic proof of the inductive formula for the Procesi bundle that plays an important role in Haiman's construction. Then we use the inductive formula to prove a weaker version of the $n!$ theorem: the normalization of Ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05862","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":""},"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"}