{"paper":{"title":"A combinatorial study of affine Schubert varieties in affine Grassmannian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO","math.GR"],"primary_cat":"math.RT","authors_text":"Jiuzu Hong, Marc Besson","submitted_at":"2019-06-21T21:49:30Z","abstract_excerpt":"Let $\\overline{\\mathtt{X}}_\\lambda$ be the closure of the $\\mathtt{I}$-orbit $\\mathtt{X}_\\lambda$ in the affine Grassmanian $\\mathtt{Gr}$ of a simple algebraic group $G$ of adjoint type, where $\\mathtt{I}$ is the Iwahori group and $\\lambda$ is a coweight of $G$. We find a simple algorithm which describes the set $\\Psi(\\lambda)$ of all $\\mathtt{I}$-orbits in $\\overline{\\mathtt{X}}_\\lambda$ in terms of coweights. We introduce $R$-operators (associated to positive roots) on the coweight lattice of $G$, which exactly describe the closure relation of $\\mathtt{I}$-orbits. These operators satisfy Bra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09341","kind":"arxiv","version":3},"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/1906.09341/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"}