A Boson-fermion Realization of Highest Weight Modules over \(\mathfrak{g}\widetilde{\mathfrak{l}_{M/N}}(\theta)\)

Abstract

In this paper, we construct a superfermionic representation as well as a vertex representation for twisted general linear affine Lie superalgebras. We also establish a module isomorphism between them, which generalizes the super boson-fermion correspondence of type B given by Kac-van de Leur. Based on this isomorphism, we determine explicitly the irreducible components of these two representations. Particularly, we obtain in this way two kinds of systematic construction of level 1 irreducible integrable highest weight modules for twisted general linear affine Lie superalgebras.