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

TL;DR

This paper constructs a novel quantum fermion realization of the finite dimensional spinor representation of the quantum supergroup ${ m{U}}_q({ m{osp}}(1|2n))$, and extends it to infinite dimensional cases using quantum bosons and fermions.

Contribution

It introduces a new realization of the quantum supergroup's spinor representations on Fock space, differing from previous methods, including for infinite dimensional cases.

Findings

Constructed a fermionic realization on Fock space.

Extended the realization to infinite dimensional representations.

Provided a new approach different from prior research.

Abstract

The quantum supergroup ${\rm{U}}_q({\mathfrak {osp}}(1|2n))$ 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 ${\rm{U}}_q({\mathfrak {osp}}(2m+1|2n))$ 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.