{"paper":{"title":"Monoidal categories associated with strata of flag manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Euiyong Park, Masaki Kashiwara, MyungHo Kim, Se-Jin Oh","submitted_at":"2017-08-15T08:23:26Z","abstract_excerpt":"We construct a monoidal category $\\mathscr{C}_{w,v}$ which categorifies the doubly-invariant algebra $^{N'(w)}\\mathbb{C}[N]^{N(v)}$ associated with Weyl group elements $w$ and $v$. It gives, after a localization, the coordinate algebra $\\mathbb{C}[\\mathcal{R}_{w,v}]$ of the open Richardson variety associated with $w$ and $v$. The category $\\mathscr{C}_{w,v}$ is realized as a subcategory of the graded module category of a quiver Hecke algebra $R$. When $v= \\mathrm{id}$, $\\mathscr{C}_{w,v}$ is the same as the monoidal category which provides a monoidal categorification of the quantum unipotent c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04428","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"}