{"paper":{"title":"Highest weight vectors of mixed tensor products of general linear Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Hebing Rui, Yucai Su","submitted_at":"2014-02-06T00:56:56Z","abstract_excerpt":"In this paper, a notion of cyclotomic (or level $k$) walled Brauer algebras $\\mathscr B_{k, r, t}$ is introduced for arbitrary positive integer $k$. It is proven that $\\mathscr B_{k, r, t}$ is free over a commutative ring with rank $k^{r+t}(r+t)!$ if and only if it is admissible. Using super Schur-Weyl duality between general linear Lie superalgebras $\\mathfrak{gl}_{m|n}$ and $\\mathscr B_{2, r, t}$, we give a classification of highest weight vectors of $\\mathfrak{gl}_{m|n}$-modules $M_{pq}^{rt}$, the tensor products of Kac-modules with mixed tensor products of the natural module and its dual. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1221","kind":"arxiv","version":1},"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"}