不变量理论与具有负整数中心荷的W_{1+\infty}代数
Invariant theory and the W_{1+\infty} algebra with negative integral central charge
摘要：
中心荷为c的顶点代数W_{1+\infty,c}可以定义为圆上微分算子李代数的泛中心扩张上的模.对于整数n的\geq 1，物理学文献中证明了W_{1+\infty,-n}应该有一个由n^2+2n个元素组成的极小强生成集.利用Kac-Radul的W_{1+\infty,-n}的自由场实现，结合GL_n标准表示的Weyl不变理论第一和第二基本定理的变形形式，证明了这个猜想.结果是W_{1+\infty,-n}的不可约最高权表示被C^{n^2+2n}的闭子簇参数化。
英文摘要：
The vertex algebra W_{1+\infty,c} with central charge c may be defined as a module over the universal central extension of the Lie algebra of differential operators on the circle. For an integer n\geq 1, it was conjectured in the physics literature that W_{1+\infty,-n} should have a minimal strong generating set consisting of n^2+2n elements. Using a free field realization of W_{1+\infty,-n} due to Kac-Radul, together with a deformed version of Weyl's first and second fundamental theorems of invariant theory for the standard representation of GL_n, we prove this conjecture. A consequence is that the irreducible, highest-weight representations of W_{1+\infty,-n} are parametrized by a closed subvariety of C^{n^2+2n}.
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