Abstract
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.
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Cheng, SJ., Wang, W. Howe Duality for Lie Superalgebras. Compositio Mathematica 128, 55–94 (2001). https://doi.org/10.1023/A:1017594504827
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DOI: https://doi.org/10.1023/A:1017594504827