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ISSN 1088-6850(e) ISSN 0002-9947(p)

Quasi-finite modules for Lie superalgebras of infinite rank

Authors: Ngau Lam and R. B. Zhang
Journal: Trans. Amer. Math. Soc. 358 (2006), 403-439
MSC (2000): Primary 17B65, 17B10
Posted: July 26, 2005
MathSciNet review: 2171240
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Abstract: We classify the quasi-finite irreducible highest weight modules over the infinite rank Lie superalgebras $\widehat{\rm gl}_{\infty\vert\infty}$ , $\widehat{\mathcal{C}}$ and $\widehat{\mathcal{ D}}$ , 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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