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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Quasi-finite modules for Lie superalgebras of infinite rank
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by Ngau Lam and R. B. Zhang PDF
Trans. Amer. Math. Soc. 358 (2006), 403-439 Request permission

Abstract:

We classify the quasi-finite irreducible highest weight modules over the infinite rank Lie superalgebras $\widehat {\mathrm {gl}}_{\infty |\infty }$, $\widehat {\mathcal {C}}$ 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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Additional Information
  • 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
  • Received by editor(s): October 30, 2003
  • Received by editor(s) in revised form: June 11, 2004
  • Published electronically: 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 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 403-439
  • MSC (2000): Primary 17B65, 17B10
  • DOI: https://doi.org/10.1090/S0002-9947-05-03795-5
  • MathSciNet review: 2171240