{"paper":{"title":"Macdonald polynomials, Laumon spaces and perverse coherent sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.AG","authors_text":"Alexander Braverman, Jun'ichi Shiraishi, Michael Finkelberg","submitted_at":"2012-06-14T15:11:00Z","abstract_excerpt":"Let $G$ be an almost simple simply connected complex Lie group, and let $G/U_-$ be its base affine space. In this paper we formulate a conjecture, which provides a new geometric interpretation of the Macdonald polynomials associated to $G$ via perverse coherent sheaves on the scheme of formal arcs in the affinization of $G/U_-$. We prove our conjecture for $G=SL(N)$ using the so called Laumon resolution of the space of quasi-maps (using this resolution one can reformulate the statement so that only \"usual\" (not perverse) coherent sheaves are used). In the course of the proof we also give a $K$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3131","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"}