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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 \\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.02176","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-09T14:00:22Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"9319e0422b14e0afc326bcf7f6d3ea6a8794289e218e39d576d58962344a3cfe","abstract_canon_sha256":"9cb752f0dfb774e7f585c4d0235909f91cd1d36ea8d381b745499b36d4abaf19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:00.303083Z","signature_b64":"JDHAnZVJtbO7EXFCe+h5Y8z5+bmMDWEVDrU/MquOJ2w9L0fEYQoPrjQnJabJmk5KNpkj5ofeCJVefa8AmN9bCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5457ac5459b12f0b83effbf624c657d6fd50c0c4bf82c68a5b1381105d6e542c","last_reissued_at":"2026-05-18T00:53:00.302547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:00.302547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathfrak g$. 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