Highest weight irreducible unitary representations of Lie algebras of infinite matrices. I. The algebra gl(∞)

Abstract

Two classes of irreducible highest weight modules of the general linear Lie algebra gl(∞), corresponding to two different Borel subalgebras, are constructed. Both classes contain all unitary representations. Within each module a basis is introduced. Expressions for the transformation of the basis under the action of the algebra are written down.