{"paper":{"title":"Bimodule structure of the mixed tensor product over $U_{q} s\\ell(2|1)$ and quantum walled Brauer algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"A.M. Kiselev, D.V. Bulgakova, I.Yu. Tipunin","submitted_at":"2017-04-28T13:28:19Z","abstract_excerpt":"We study a mixed tensor product $\\mathbf{3}^{\\otimes m} \\otimes \\mathbf{\\overline{3}}^{\\otimes n}$ of the three-dimensional fundamental representations of the Hopf algebra $U_{q} s\\ell(2|1)$, whenever $q$ is not a root of unity. Formulas for the decomposition of tensor products of any simple and projective $U_{q} s\\ell(2|1)$-module with the generating modules $\\mathbf{3}$ and $\\mathbf{\\overline{3}}$ are obtained. The centralizer of $U_{q} s\\ell(2|1)$ on the chain is calculated. It is shown to be the quotient $\\mathscr{X}_{m,n}$ of the quantum walled Brauer algebra. The structure of projective "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08921","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"}