{"paper":{"title":"On the tensor semigroup of affine kac-moody lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Nicolas Ressayre (ICJ)","submitted_at":"2017-01-09T14:00:22Z","abstract_excerpt":"In this paper, we are interested in the decomposition of the tensor product of two representations of a symmetrizable Kac-Moody Lie algebra $\\mathfrak g$. Let $P\\_+$ be the set of dominant integral weights. For $\\lambda\\in P\\_+$ , $L(\\lambda)$ denotes the irreducible, integrable, highest weight representation of g with highest weight $\\lambda$. Let $P\\_{+,\\mathbb Q}$ be the rational convex cone generated by $P\\_+$. Consider the tensor cone $\\Gamma(\\mathfrak g) := \\{(\\lambda\\_1 ,\\lambda\\_2, \\mu) $\\in$ P\\_{+,\\mathbb Q}^3\\,| \\exists N \\textgreater{} 1 L(N\\mu) \\subset  L(N \\lambda\\_1)\\otimes L(N \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02176","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"}