Unitary highest weight representations of quantum general linear superalgebra

Fock space realisations of unitary highest weight representations of compact and noncompact real forms of the quantum general linear superalgebra Uq(glm|n) are constructed. We decompose all tensor powers of the Fock spaces into direct sums of irreducible unitary submodules for compact or noncompact real forms of the quantum superalgebra, obtaining multiplicities of the irreducibles and also explicit formulae for their highest weight vectors. A generalised Howe duality of type (Uq(glm|n),Uq(glk)) is also established, which is used in the study of unitary representations and should also be of independent interest.