Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: July 26, 2005
MathSciNet review: 2171240
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 17B65, 17B10

Retrieve articles in all journals with MSC (2000): 17B65, 17B10


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

DOI: http://dx.doi.org/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
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.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.