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

##### J. Algebr. Comb. 28(4), 439-459 (2008)
DOI: 10.1007/s10801-007-0109-9

### Summary

Summary: 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 $\frak gl _{ m | n}$ frakgl_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.

### Keywords/Phrases

keywords hook Schur polynomial, Lie superalgebra, character formula