仿射ADE中岛颤振品种在纤维折叠中的欧拉特性

IF 1.2 2区 数学 Q1 MATHEMATICS
Lukas Bertsch, Ádám Gyenge, Balázs Szendrői
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引用次数: 0

摘要

我们通过研究GIT图的相关变化中的折叠纤维,证明了与仿射ADE图相关的中岛颤振品种在一般和某些非一般稳定性条件下产生欧拉特征序列的一个通用替代公式,统一和推广了前两位作者与n和Nakajima的早期结果。作为一种特殊情况,我们计算了Kleinian轨道的非交换Quot格式的欧拉特征的生成序列。在类型A和秩1中,我们用环面局部化和划分枚举给出了替换公式的第二个组合证明。这给出了GIT映射变化纤维的组合模型,并导致我们的结果与a型仿射李代数和有限李代数的表示理论之间的关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Euler characteristics of affine ADE Nakajima quiver varieties via collapsing fibres

Euler characteristics of affine ADE Nakajima quiver varieties via collapsing fibres

Euler characteristics of affine ADE Nakajima quiver varieties via collapsing fibres

Euler characteristics of affine ADE Nakajima quiver varieties via collapsing fibres

Euler characteristics of affine ADE Nakajima quiver varieties via collapsing fibres

We prove a universal substitution formula that compares generating series of Euler characteristics of Nakajima quiver varieties associated with affine ADE diagrams at generic and at certain non-generic stability conditions via a study of collapsing fibres in the associated variation of GIT map, unifying and generalising earlier results of the last two authors with Némethi and of Nakajima. As a special case, we compute generating series of Euler characteristics of non-commutative Quot schemes of Kleinian orbifolds. In type A and rank 1, we give a second, combinatorial proof of our substitution formula, using torus localisation and partition enumeration. This gives a combinatorial model of the fibres of the variation of GIT map, and also leads to relations between our results and the representation theory of the affine and finite Lie algebras in type A.

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来源期刊
CiteScore
1.90
自引率
0.00%
发文量
186
审稿时长
6-12 weeks
期刊介绍: The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.
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