论文标题
$ \ mathbb {a}^2 $中的积分混洗代数和$ k $ - 希尔伯特方案的理论
The integral shuffle algebra and the $K$-theory of the Hilbert scheme of points in $\mathbb{A}^2$
论文作者
论文摘要
We examine the shuffle algebra defined over the ring $\mathbf{R} = \mathbb{C}[q_1^{\pm 1}, q_2^{\pm 1}]$, also called the integral shuffle algebra, which was found by Schiffmann and Vasserot to act on the equivariant $K$-theory of the Hilbert scheme of points in the plane.我们发现，有限地生成了积分混洗代数的2和3变量元素的模块，并证明了元素在任意许多变量任意变量的积分shuffle代数中的必要条件。
We examine the shuffle algebra defined over the ring $\mathbf{R} = \mathbb{C}[q_1^{\pm 1}, q_2^{\pm 1}]$, also called the integral shuffle algebra, which was found by Schiffmann and Vasserot to act on the equivariant $K$-theory of the Hilbert scheme of points in the plane. We find that the modules of 2 and 3 variable elements of the integral shuffle algebra are finitely generated and prove a necessary condition for an element to be in the integral shuffle algebra for arbitrarily many variables.
