{"paper":{"title":"The torus equivariant cohomology rings of Springer varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Hiraku Abe, Tatsuya Horiguchi","submitted_at":"2014-04-04T11:22:43Z","abstract_excerpt":"The Springer variety of type $A$ associated to a nilpotent operator on $\\mathbb{C}^n$ in Jordan canonical form admits a natural action of the $\\ell$-dimensional torus $T^{\\ell}$ where $\\ell$ is the number of the Jordan blocks. We give a presentation of the $T^{\\ell}$-equivariant cohomology ring of the Springer variety through an explicit construction of an action of the $n$-th symmetric group on the $T^{\\ell}$-equivariant cohomology group. The $T^{\\ell}$-equivariant analogue of so called Tanisaki's ideal will appear in the presentation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1217","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":""},"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"}