顶点算子、格拉斯曼算子和希尔伯特格式
Vertex Operators, Grassmannians, and Hilbert Schemes
摘要：
我们描述了一个著名的收集顶点运营商的无限楔形表示的限制几何对应的等变上同调群的有限维近似的佐藤格拉斯曼，在高和低程度的截止。我们证明，本地化，玻色子费米子对应，和交织的关系与Virasoro代数的本地化表达式的限制，这些运营商的组成。然后，我们表明，这些运营商，几乎通过定义，希尔伯特计划顶点运营商定义的Okounkov和作者在\cite{CO}时，表面是$\mathbb{C}^2$与环面行动$z\cdot (x,y) = (zx,z^{-1}y)$。
英文摘要：
We describe a well-known collection of vertex operators on the infinite wedge representation as a limit of geometric correspondences on the equivariant cohomology groups of a finite-dimensional approximation of the Sato grassmannian, by cutoffs in high and low degrees. We prove that locality, the boson-fermion correspondence, and intertwining relations with the Virasoro algebra are limits of the localization expression for the composition of these operators. We then show that these operators are, almost by definition, the Hilbert scheme vertex operators defined by Okounkov and the author in \cite{CO} when the surface is $\mathbb{C}^2$ with the torus action $z\cdot (x,y) = (zx,z^{-1}y)$.
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