A quantum fermion realisation of the finite dimensional spinor representation of ${\mathrm{U}}_q(\mathfrak{osp}(1|2n))$

Abstract

The quantum supergroup ${\mathrm{U}}_q(\mathfrak{osp}(1|2n))$ 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 ${\mathrm{U}}_q(\mathfrak{osp}(2m+1|2n))$ for $m,n\ge 1$ by using both quantum bosons and fermions. This leads to a new realisation different from those obtained before by other researchers.

17 pages