Highest weight irreducible unitarizable representations of Lie algebras of infinite matrices. The algebra A∞

Abstract

In this paper all unitarizable irreducible highest weight representations of the infinite-dimensional Lie algebra A∞, which is a completion and central extension of the general linear Lie algebra gl∞, are considered. Within each representation space a basis is introduced and expressions for the transformations of the basis under the action of the Chevalley generators are written.