Classification of quasifinite modules over Lie algebras of matrix differential operators on the circle
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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.References
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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
- 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
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 1949-1957
- MSC (2000): Primary 17B10, 17B65, 17B66, 17B68
- DOI: https://doi.org/10.1090/S0002-9939-05-07881-0
- MathSciNet review: 2137860