Howe Duality for Lie Superalgebras

Simple item page
dc.creatorCheng, Shun-Jen
dc.creatorWang, Weiqiang
dc.date2000-08-13
dc.date.accessioned2026-07-07T04:36:46Z
dc.date.available2026-07-07T04:36:46Z
dc.descriptionWe study a dual pair of general linear Lie superalgebras in the sense of R. Howe. We give an explicit multiplicity-free decomposition of a symmetric and skew-symmetric algebra (in the super sense) under the action of the dual pair and present explicit formulas for the highest weight vectors in each isotypic subspace of the symmetric algebra. We give an explicit multiplicity-free decomposition into irreducible $gl(m|n)$-modules of the symmetric and skew-symmetric algebras of the symmetric square of the natural representation of $gl(m|n)$. In the former case we find as well explicit formulas for the highest weight vectors. Our work unifies and generalizes the classical results in symmetric and skew-symmetric models and admits several applications.
dc.description41 pages, LaTeX format, to appear in Compositio Math
dc.identifierhttps://arxiv.org/abs/math/0008093
dc.identifierhttp://arxiv.org/abs/math/0008093
dc.identifierCompositio Math.128 (2001) 55-94
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59720
dc.subjectRepresentation Theory
dc.subject17B67
dc.titleHowe Duality for Lie Superalgebras
dc.typetext

Files

Collections

arXiv