{"paper":{"title":"Three presentations of torus equivariant cohomology of flag manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Shizuo Kaji","submitted_at":"2015-04-05T07:09:08Z","abstract_excerpt":"Let $G$ be a compact connected Lie group and $T$ be its maximal torus. The homogeneous space $G/T$ is called the (complete) flag manifold. One of the main goals of the {\\em equivariant Schubert calculus} is to study the $T$-equivariant cohomology $H^*_T(G/T)$ with regard to the $T$-action on $G/T$ by multiplication. There are three presentations known for $H^*_T(G/T)$; (1) the free $H^*(BT)$-module generated by the Schubert varieties (2) (with the rational coefficients) the {\\em double coinvariant ring} of the Weyl group (3) the {\\em GKM ring} associated to the Hasse graph of the Weyl group. E"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01091","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"}