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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Classification of quasifinite modules over Lie algebras of matrix differential operators on the circle


Author: Yucai Su
Journal: Proc. Amer. Math. Soc. 133 (2005), 1949-1957
MSC (2000): Primary 17B10, 17B65, 17B66, 17B68
Published electronically: January 31, 2005
MathSciNet review: 2137860
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Abstract: We prove that an irreducible quasifinite module over the central extension of the Lie algebra of $N\times N$-matrix differential operators on the circle is either a highest or lowest weight module or else a module of the intermediate series. Furthermore, we give a complete classification of indecomposable uniformly bounded modules.


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Additional Information

Yucai Su
Affiliation: Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, People’s Republic of China — and — Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Email: ycsu@sjtu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07881-0
PII: S 0002-9939(05)07881-0
Received by editor(s): February 3, 2003
Received by editor(s) in revised form: April 1, 2004
Published electronically: January 31, 2005
Additional Notes: The author was supported by an NSF grant 10171064 of China and two grants, “Excellent Young Teacher Program” and “Trans-Century Training Programme Foundation for the Talents”, from the Ministry of Education of China.
Communicated by: Dan M. Barbasch
Article copyright: © Copyright 2005 American Mathematical Society