Transactions of the American Mathematical Society

Author(s): Ngau Lam; R. B. Zhang
Journal: Trans. Amer. Math. Soc. 358 (2006), 403-439.
MSC (2000): Primary 17B65, 17B10
Posted: July 26, 2005
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 17B65, 17B10

Ngau Lam
Affiliation: Department of Mathematics, National Cheng Kung University, Tainan, Taiwan 701
Email: nlam@mail.ncku.edu.tw

R. B. Zhang
Affiliation: School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia
Email: rzhang@maths.usyd.edu.au

DOI: 10.1090/S0002-9947-05-03795-5
PII: S 0002-9947(05)03795-5
Keywords: Infinite rank Lie superalgebras, quasi-finite representations, unitarizable representations, character formulae
Received by editor(s): October 30, 2003
Received by editor(s) in revised form: June 11, 2004
Posted: July 26, 2005
Additional Notes: The first author was partially supported by NSC-grant 92-2115-M-006-016 of the R.O.C
The second author was partially supported by the Australian Research Council.
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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