Abstract
In our paper [KR] we began a systematic study of representations of the universal central extension
of the Lie algebra of differential operators on the circle. This study was continued in the paper [FKRW] in the framework of vertex algebra theory. It was shown that the associated to
simple vertex algebraW
1+∞,N
with positive integral central chargeN is isomorphic to the classical vertex algebraW(gl
N), which led to a classification of modules overW
1+∞,N
. In the present paper we study the remaing nontrivial case, that of a negative central charge-N. The basic tool is the decomposition ofN pairs of free charged bosons with respect togl
N and the commuting withgl
N Lie algebra of infinite matricesĝl.
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To Alexander Alexandrovich Kirillov on his 60-th birthday
Supported in part by NSF grant DMS-9103792.
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Kac, V., Radul, A. Representation theory of the vertex algebraW 1+∞ . Transformation Groups 1, 41–70 (1996). https://doi.org/10.1007/BF02587735
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DOI: https://doi.org/10.1007/BF02587735