Highest weight representations for gl(m/n) and gl(m+n)

It is shown how vector coherent state (VCS) theory enlightens the simultaneous discussion of representation theory for classical Lie algebras and superalgebras and provides an optimal framework for the explanation of the noted similarities and dissimilarities of their representations. Reducibility, atypicality, and the positive-definitiveness of inner products in VCS representation spaces are discussed. The discussion is exemplified through the parallel and explicit construction of highest weight ladder representations of the Lie algebra gl(m+n) and superalgebra gl(m/n) in gl(m)⊕gl(n) bases.