Gel’fand–Zetlin basis for a class of representations of the Lie superalgebra

Abstract

A new, so called odd Gel’fand–Zetlin (GZ) basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra . The related GZ patterns are based upon the decomposition according to a particular chain of subalgebras of . This chain contains only genuine Lie superalgebras of type with k and l nonzero (apart from the final element of the chain which is ). Explicit expressions for a set of generators of the algebra on this GZ basis are determined. The results are extended to an explicit construction of a class of irreducible highest weight modules of the general linear Lie superalgebra .