Howe Duality for Lie Superalgebras

@inproceedings{Wang2008HoweDF,
  title={Howe Duality for Lie Superalgebras},
  author={Wei-Qiang Wang},
  year={2008}
}
We 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 skewsymmetric algebras of the symmetric square of… CONTINUE READING