Fermionic representations of unitary Lie algebras coordinated by skew rings

Abstract

Let $\sigma$ be a character from an abelian group to $\mathbb C^*$, and let $\mathcal R_\sigma$ be the skew Laurent polynomial ring associated to it. In this paper, the fermionic representation of Allison-Faulkner type unitary Lie algebra coordinated by $\mathcal R_\sigma$ is constructed and its irreducible components are determined explicitly.