{"paper":{"title":"Posets, Tensor Products and Schur positivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Daisuke Sagaki, Ghislain Fourier, Vyjayanthi Chari","submitted_at":"2012-10-23T10:33:30Z","abstract_excerpt":"Let g be a complex finite-dimensional simple Lie algebra. Given a positive integer k and a dominant weight \\lambda, we define a preorder on the set $P(\\lambda, k)$ of k-tuples of dominant weights which add up to \\lambda. Let $P(\\lambda, k)/\\sim$ be the corresponding poset of equivalence classes defined by the preorder. We show that if \\lambda is a multiple of a fundamental weight (and k is general) or if k=2 (and \\lambda is general), then $P(\\lambda, k)/\\sim$ coincides with the set of S_k-orbits in $P(\\lambda,k)$, where S_k acts on $P(\\lambda, k)$ as the permutations of components. If g is of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6184","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"}