Howe Duality for Lie Superalgebras

By Shun-Jen Cheng, Weiqiang Wang. Compositio Mathematica, 2000

76 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/521e7f470c03e03e53872ac759a6d0b3c19e8d98

Citations in the corpus

• Super $q$-Howe duality and web categories (2015, unknown): “Note that the nonquantum version of Theorem 3.6 can be found for example in [4, Theorem 3.3] or [28, Proposition 2.2].”