A 型中箭图簇、环路 Grassmannian 与幂零锥的比较
表示论
2025-03-18 v2
摘要
在 A 型中，我们找到了出现于三种情形下的几何之间的等价性：Nakajima 的（“框架化”）箭图簇、矩阵共轭类与环路 Grassmannian。这些现在均由显式公式给出。特别地，我们将框架化箭图簇嵌入 Beilinson-Drinfeld Grassmannian。这为 Nakajima 簇提供了紧化，并将仿射 Grassmannian 分解为 Nakajima 簇。作为一个应用，我们给出了对称与斜对称 对偶的几何版本。
引用
@article{arxiv.1905.01810,
title = {Comparison of quiver varieties, loop Grassmannians and nilpotent cones in type A},
author = {Ivan Mirkovic and Maxim Vybornov},
journal= {arXiv preprint arXiv:1905.01810},
year = {2025}
}
备注
Some of the results of this paper have appeared in arXiv:0712.4160. The new results are the explicit isomorphism of quiver varieties and loop Grassmannians and a much better understanding of the relation of loop Grassmannians and nilpotent cones. The paper has also been extensively rewritten. Final published version