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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 $\frak{gl}_{m|n}$ . 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.

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