By using the Y(gl(m/n)) super Yangian symmetry of the SU(m/n) supersymmetric Haldane-Shastry spin chain, we show that the partition function of this model satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom. As a by product of this study of the duality relation, we find a novel combinatorial formula for the super Schur polynomials associated with some irreducible representations of the Y(gl(m/n)) Yangian algebra. Finally, we reveal an intimate connection between the Global SU(m/n) symmetry of a spin chain and the boson-fermion duality relation. (c) 2007 Elsevier B.V. All rights reserved.