Highest weight irreducible representations of the Lie superalgebra $gl(1/\infty)$

TL;DR

This paper constructs two classes of irreducible highest weight modules for the infinite-dimensional Lie superalgebra $gl(1/ olinebreak\infty)$, providing explicit bases and transformation relations under algebra generators.

Contribution

It introduces explicit constructions of two classes of irreducible modules for $gl(1/ olinebreak\infty)$, including bases and action formulas, advancing understanding of its representation theory.

Findings

Two classes of irreducible highest weight modules are constructed.

Explicit bases and transformation relations are provided.

The structure of modules under the algebra's action is detailed.

Abstract

Two classes of irreducible highest weight modules of the general linear Lie superalgebra $gl(1/\infty)$ are constructed. Within each module a basis is introduced and the transformation relations of the basis under the action of the algebra generators are written down.