A quantum fermion realisation of the finite dimensional spinor representation of Uq(osp(1|2n))

Abstract

The quantum supergroup Uq(osp(1|2n)) admits a finite dimensional spinor representation, which does not have a classical limit. We construct a realisation of this representation on the Fock space of q-fermions. We also generalise the construction to the infinite dimensional spinor representations of Uq(osp(2m+1|2n)) for m,n≥1 by using both quantum bosons and fermions. This leads to a new realisation different from those obtained before by other researchers.