Gel'fand-Zetlin basis for a class of representations of the Lie superalgebra gl (infinity vertical bar infinity)

摘要

A new, so called odd Gel'fand-Zetlin (GZ) basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra gl(n vertical bar n). The related GZ patterns are based upon the decomposition according to a particular chain of subalgebras of gl(n vertical bar n). This chain contains only genuine Lie super-algebras of type gl(k vertical bar l) with k and l nonzero (apart from the final element of the chain which is gl(1 vertical bar 0) equivalent to gl(1)). 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 gl(infinity vertical bar infinity).