Representations of Toroidal general linear Superalgebra

TL;DR

This paper introduces a faithful vertex operator and boson-based representation of the toroidal superalgebra, a universal central extension of the general linear superalgebra tensor Laurent polynomials, expanding algebraic understanding.

Contribution

It provides the first explicit faithful representation of the toroidal superalgebra using vertex operators and bosons, advancing the study of superalgebra representations.

Findings

Constructed a faithful representation of the toroidal superalgebra.

Utilized vertex operators and bosons in the representation.

Enhanced understanding of the structure of toroidal superalgebras.

Abstract

We consider general linear superalgebra (type A) and tensor with Laurent polynomial ring in several variables. We then consider the universal central extension of this Lie superalgebra which we call toroidal superalgebra. We give a faithful representation of toroidal superalgebra using vertex operators and bosons.