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1 results

  • Howe Duality for Lie Superalgebras

  • Shun-Jen Cheng, Weiqiang Wang
  • Journal:
    Compositio Mathematica / Volume 128 / Issue 1 / August 2001
    Published online by Cambridge University Press:
    04 December 2007, pp. 55-94
    Print publication:
    August 2001
    • Article
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  • 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 skew-symmetric algebras of the symmetric square of the natural representation of gl(m|n). In the former case, we also find 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.