{"paper":{"title":"Mixed Schur-Weyl-Sergeev duality for queer Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Ji Hye Jung, Seok-Jin Kang","submitted_at":"2012-08-25T15:14:51Z","abstract_excerpt":"We introduce a new family of superalgebras $\\overrightarrow{B}_{r,s}$ for $r, s \\ge 0$ such that $r+s>0$, which we call the walled Brauer superalgebras, and prove the mixed Scur-Weyl-Sergeev duality for queer Lie superalgebras. More precisely, let $\\mathfrak{q}(n)$ be the queer Lie superalgebra, ${\\mathbf V} =\\mathbb{C}^{n|n}$ the natural representation of $\\mathfrak{q}(n)$ and ${\\mathbf W}$ the dual of ${\\mathbf V}$. We prove that, if $n \\ge r+s$, the superalgebra $\\overrightarrow{B}_{r,s}$ is isomorphic to the supercentralizer algebra $_{\\mathfrak{q}(n)}({\\mathbf V}^{\\otimes r} \\otimes {\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5139","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"}