Higher spin sl_2 R-matrix from equivariant (co)homology
Higher spin sl_2 R-matrix from equivariant (co)homology
复制标题
来自等变（共）同调的更高自旋 sl_2 R 矩阵
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
P. Zinn
中科院分区：
文献类型：
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作者：
D. Bykov;P. Zinn
我们使用一种类似于莫利克（Maulik）和奥昆科夫（Okounkov）的方法，即通过研究某些代数簇的等变（上）同调，计算作用在两个自旋为\(\frac{\ell}{2}\)（\(\ell\in\mathbb{N}\)）表示的乘积上的有理\(\mathfrak{sl}_2\) \(R\)-矩阵。这些簇首先由涅克拉索夫（Nekrasov）和沙塔什维利（Shatashvili）考虑，它们通常是奇异的。它们可被视为\(A_1\)中岛箭图簇（即格拉斯曼流形的余切丛）的高自旋推广，后者对应于\(\ell = 1\)。
We compute the rational $\mathfrak{sl}_2$ $R$-matrix acting in the product of two spin-$\ell\over 2$ (${\ell \in \mathbb{N}}$) representations, using a method analogous to the one of Maulik and Okounkov, i.e., by studying the equivariant (co)homology of certain algebraic varieties. These varieties, first considered by Nekrasov and Shatashvili, are typically singular. They may be thought of as the higher spin generalizations of $A_1$ Nakajima quiver varieties (i.e., cotangent bundles of Grassmannians), the latter corresponding to $\ell=1$.