Representations of the affine ageing algebra agê(1)

Abstract

In this paper, we investigate the affine ageing algebra agê(1), which is a central extension of the loop algebra of the one-spatial ageing algebra age(1). Certain Verma-type modules including Verma modules and imaginary Verma modules of agê(1) are studied. Particularly, the simplicity of these modules are characterized and their irreducible quotient modules are determined. We also study the restricted modules of agê(1) which are also the modules of the affine vertex algebra arising from the one-spatial ageing algebra age(1). We present certain constructions of simple restricted agê(1)-modules and an explicit such example of simple restricted module via the Whittaker module of agê(1) is given.