{"paper":{"title":"On momentum images of representations and secant varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.RT","authors_text":"Elitza Hristova, Tomasz Maciazek, Valdemar V. Tsanov","submitted_at":"2015-04-05T10:33:21Z","abstract_excerpt":"Let $K$ be a connected compact semisimple group and $V_\\lambda$ be an irreducible unitary representation with highest weight $\\lambda$. We study the momentum map $\\mu:\\mathbb P(V_\\lambda)\\to\\mathfrak k^*$. The intersection $\\mu(\\mathbb P(V_\\lambda))^+=\\mu(\\mathbb P(V_\\lambda))\\cap{\\mathfrak t}^+$ of the momentum image with a fixed Weyl chamber is a convex polytope called the momentum polytope of $V_\\lambda$. We construct an affine rational polyhedral convex cone $\\Upsilon_\\lambda$ with vertex $\\lambda$, such that $\\mu(\\mathbb P(V_\\lambda))^+\\subset\\Upsilon_\\lambda \\cap {\\mathfrak t}^+$. We sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01110","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"}