箭图簇的图自同构
表示论
2014-09-23 v2
摘要
我们证明了 Nakajima 箭图簇在图自同构下的不动点子簇是 Reiten 和 Riedtmann 引入的“分裂商箭图”所对应的箭图簇的不交并。作为特例，D 型箭图簇作为 A 型箭图簇在图对合下的不动点子簇的连通分支出现。在 A 型箭图簇对应于小自对偶表示的情形下，我们证明了图对合与两行 Slodowy 簇的经典对合相一致。由此可得，某些 D 型箭图簇同构于正交或辛李代数的 Slodowy 簇。
引用
@article{arxiv.1309.0572,
title = {Diagram automorphisms of quiver varieties},
author = {Anthony Henderson and Anthony Licata},
journal= {arXiv preprint arXiv:1309.0572},
year = {2014}
}
备注
43 pages. In version 2, at the referee's suggestion, we slightly expand some statements (Theorem 1.2 and Proposition 3.19) to include the relevant affine varieties. This version is to appear in Advances in Mathematics