{"paper":{"title":"Canonical Landau-Ginzburg models for cominuscule homogeneous spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.AG","authors_text":"Charles Wang, Peter Spacek","submitted_at":"2024-10-07T14:26:32Z","abstract_excerpt":"We present a type-independent Landau-Ginzburg (LG) model $(X_\\mathrm{can}, \\mathcal{W}_\\mathrm{can})$ for any cominuscule homogeneous space $X=G/P$. We give a fully combinatorial construction for our superpotential $\\mathcal{W}_\\mathrm{can}$ as a sum of $n+1$ rational functions in the (generalized) Pl\\\"ucker coordinates on the \"Langlands dual\" minuscule homogeneous space $\\mathbb{X}=P^\\vee\\backslash G^\\vee$. Explicitly, we define the denominators $\\mathcal{D}_{i_*}$ of these rational functions using the combinatorics of order ideals of the corresponding minuscule poset, which can be interprete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.05070","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.05070/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"}