Classification of Quasifinite Modules over Lie Algebras of Matrix Differential Operators on the Circle

Details Classification of Quasifinite Modules over Lie Algebras of Matrix Differential Operators on the Circle Classification of Quasifinite Modules over Lie Algebras of Matrix Differential Operators on the Circle

2005-11-21

arxiv.org/abs/math/0511524v1

Proc. Amer. Math. Soc., 133 (2005), 1949-1957

Mathematics

Representation Theory

LaTeX, 10 pages

Scientific paper

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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