Representation theory of the vertex algebraW1+∞
Representation theory of the vertex algebraW1+∞
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DOI：
10.1007/bf02587735
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发表时间：
1996-03
影响因子：
0.7
通讯作者：
V. Kac;A. Radul
中科院分区：
文献类型：
--
作者：
V. Kac;A. Radul
在我们的论文[KR]中，我们开始系统地研究圆上微分算子李代数的泛中心扩张的表示。这一研究在文[FKRW]中是在顶点代数理论的框架内继续的。证明了具有正整数中心电荷N的单点代数W1+∞，N与经典顶点代数W(GLN)同构，从而得到了W1+∞，N上模的一个分类.本文研究了剩余的非平凡情形-负中心电荷-N.基本工具是N对自由带电玻色子关于GLN的分解和与无限矩阵的GLN李代数ĝL的交换。
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 algebra W 1+∞, N with positive integral central charge N is isomorphic to the classical vertex algebra W (gl N), which led to a classification of modules over W 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 of N pairs of free charged bosons with respect to gl N and the commuting with gl N Lie algebra of infinite matrices ĝl.