Brauer algebras, symplectic Schur algebras and Schur-Weyl duality

Simple item page
dc.creatorDipper, Richard
dc.creatorDoty, Stephen
dc.creatorHu, Jun
dc.date2005-03-24
dc.date2005-09-28
dc.date.accessioned2026-07-07T06:19:39Z
dc.date.available2026-07-07T06:19:39Z
dc.descriptionIn this paper we prove Schur-Weyl duality between the symplectic group and Brauer algebra over an arbitrary infinite field $K$. We show that the natural homomorphism from the Brauer algebra $B_n(-2m)$ to the endomorphism algebra of tensor space $(K^{2m})^{\otimes n}$ as a module over the symplectic similitude group $GSp_{2m}(K)$ (or equivalently, as a module over the symplectic group $Sp_{2m}(K)$) is always surjective. Another surjectivity, that of the natural homomorphism from the group algebra for $GSp_{2m}(K)$ to the endomorphism algebra of $(K^{2m})^{\otimes n}$ as a module over $B_n(-2m)$, is derived as an easy consequence of S.~Oehms' results [S. Oehms, J. Algebra (1) 244 (2001), 19--44].
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/math/0503545
dc.identifierhttp://arxiv.org/abs/math/0503545
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95100
dc.subjectRepresentation Theory
dc.subjectRings and Algebras
dc.subject16G99
dc.titleBrauer algebras, symplectic Schur algebras and Schur-Weyl duality
dc.typetext

Files

Collections

arXiv