{"paper":{"title":"On irreducibility of tensor products of Yangian modules associated with skew Young diagrams","license":"","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.QA","authors_text":"Maxim Nazarov, Vitaly Tarasov","submitted_at":"2000-12-06T14:11:10Z","abstract_excerpt":"We study the tensor product $W$ of any number of \"elementary\" irreducible modules $V_1,...,V_k$ over the Yangian of the general linear Lie algebra. Each of these modules is determined by a skew Young diagram and a complex parameter. For any indices $i,j=1,...,k$ there is a canonical non-zero intertwining operator $A_{ij}$ between the tensor products $V_i\\otimes V_j$ and $V_j\\otimes V_i$. This operator is defined up to a scalar multipler. We show that the tensor product $W$ is irreducible, if and only if all operators $A_{ij}$ with $i<j$ are invertible. This implies that the Yangian module $W$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0012039","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0012039/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"}