{"paper":{"title":"Affine Schubert calculus and double coinvariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Alexei Oblomkov, Erik Carlsson","submitted_at":"2018-01-27T04:44:01Z","abstract_excerpt":"We define an action of the double coinvariant algebra\n  $DR_n$ on the equivariant Borel-Moore homology of the affine flag variety\n  $\\widetilde{Fl}_n$ in type $A$, which has an explicit form in terms of\n  the left and right action of the (extended) affine Weyl group and multiplication by Chern classes.\n  Up to first order in the augmentation ideal, we show that it coincides with the\n  action of the Cherednik algebra on the equivariant homology of\n  the homogeneous affine Springer fiber $\\widetilde{S}_{n,n+1} \\subset \\widetilde{Fl}_n$\n  due to Yun and the second author, and therefore\n  preserve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09033","kind":"arxiv","version":6},"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/1801.09033/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"}