{"paper":{"title":"Stability inequalities and universal Schubert calculus of rank 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.RT"],"primary_cat":"math.GR","authors_text":"Arkady Berenstein, Michael Kapovich","submitted_at":"2010-08-10T19:04:38Z","abstract_excerpt":"The goal of the paper is to introduce a version of Schubert calculus for each dihedral reflection group W. That is, to each \"sufficiently rich'' spherical building Y of type W we associate a certain cohomology theory and verify that, first, it depends only on W (i.e., all such buildings are \"homotopy equivalent'') and second, the cohomology ring is the associated graded of the coinvariant algebra of W under certain filtration. We also construct the dual homology \"pre-ring'' of Y. The convex \"stability'' cones defined via these (co)homology theories of Y are then shown to solve the problem of c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1773","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"}