Quasi-finite modules for lie superalgebras of infinite rank

We classify the quasi-finite irreducible highest weight modules over the infinite rank Lie superalgebras down curve signgl_∞|∞, down curve sign̂ and D̂, and determine the necessary and sufficient conditions for such modules to be unitarizable. The unitarizable irreducible modules are constructed in terms of Fock spaces of free quantum fields, and explicit formulae for their formal characters are also obtained by investigating Howe dualities between the infinite rank Lie superalgebras and classical Lie groups.