A combinatorial proof of a Weyl type formula for hook Schur polynomials

In this paper, we present a simple combinatorial proof of a Weyl type formula for hook Schur polynomials, which was obtained previously by other people using a Kostant type cohomology formula for . In general, we can obtain in a combinatorial way a Weyl type character formula for various irreducible highest weight representations of a Lie superalgebra, which together with a general linear algebra forms a Howe dual pair. This research was supported by 2007 research fund of University of Seoul.