Quasi-finite representations,free field realizations,and character formulae of Lie superalgebras of infinite rank

Details Quasi-finite representations,free field realizations,and character formulae of Lie superalgebras of infinite rank Quasi-finite representations,free field realizations,and character formulae of Lie superalgebras of infinite rank

2003-11-07

arxiv.org/abs/math/0311096v1

Mathematics

Quantum Algebra

57 pages

Scientific paper

We classify the quasi-finite irreducible highest weight modules over the infinite rank Lie superalgebras $\hgltwo$, $\hC$ and $\hD$, and determine the necessary and sufficient conditions for quasi-finite irreducible highest weight modules to be unitarizable with respect to natural $\ast$-structures of the Lie superalgebras. 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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