2000/08/13 by Shun-Jen Cheng, Weiqiang Wang · 3 citations
Mathematics · #math.RT #msc:17B67
published as Compositio Math.128 (2001) 55-94 · 41 pages, LaTeX format, to appear in Compositio Math
arxiv created 2000/08/13 · arxiv updated 2009/11/30
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 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.