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

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

2006-12-29

arxiv.org/abs/math/0612845v2

Mathematics

Representation Theory

21 pages

Scientific paper

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

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