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

Abstract

In this paper, we present a simple combinatorial proof of a Weyl type formula for hook Schur polynomials, which has been obtained by using a Kostant type cohomology formula for ${\mathfrak{gl}}_{m|n}$. In general, we can obtain in a combinatorial way a Weyl type formula for various highest weight representations of a Lie superalgebra, which together with a general linear algebra forms a Howe dual pair.

21 pages