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 byproduct 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.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics