{"paper":{"title":"Affine Demazure Weight Polytopes and Twisted Bruhat Orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.RT","authors_text":"Joshua Kiers, Marc Besson, Sam Jeralds","submitted_at":"2024-04-04T01:28:56Z","abstract_excerpt":"For an untwisted affine Kac-Moody Lie algebra $\\mathfrak{g}$ with Cartan and Borel subalgebras $\\mathfrak{h} \\subset \\mathfrak{b} \\subset \\mathfrak{g}$, affine Demazure modules are certain $U(\\mathfrak{b})$-submodules of the irreducible highest-weight representations of $\\mathfrak{g}$. We introduce here the associated affine Demazure weight polytopes, given by the convex hull of the $\\mathfrak{h}$-weights of such a module. Using methods of geometric invariant theory, we determine inequalities which define these polytopes; these inequalities come in three distinct flavors, specified by the stan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.03142","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/2404.03142/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"}