Abstract
We classify the quasi-finite irreducible highest weight modules over the infinite rank Lie superalgebras gl∞ | ∞, & and D, 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.
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