Instantons and Bows for the Classical Groups

IF 0.6 4区 数学 Q3 MATHEMATICS
Sergey A Cherkis;Jacques Hurtubise
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引用次数: 1

Abstract

The construction of Atiyah, Drinfeld, Hitchin and Manin provided complete description of all instantons on Euclidean four-space. It was extended by Kronheimer and Nakajima to instantons on ALE spaces, resolutions of orbifolds $\mathbb{R}^4/\Gamma$ by a finite subgroup Γ⊂SU(2). We consider a similar classification, in the holomorphic context, of instantons on some of the next spaces in the hierarchy, the ALF multi-Taub-NUT manifolds, showing how they tie in to the bow solutions to Nahm’s equations via the Nahm correspondence. Recently Nakajima and Takayama constructed the Coulomb branch of the moduli space of vacua of a quiver gauge theory, tying them to the same space of bow solutions. One can view our construction as describing the same manifold as the Higgs branch of the mirror gauge theory as described by Cherkis, O’Hara and Saemann. Our construction also yields the monad construction of holomorphic instanton bundles on the multi-Taub-NUT space for any classical compact Lie structure group.
古典团体的瞬间和弓
Atiyah、Drinfeld、Hitchin和Manin的构造提供了欧几里得四空间上所有实例的完整描述。Kronheimer和Nakajima将其扩展到ALE空间上的实例,由有限子群Γ∧SU(2)分解出的轨道$\mathbb{R}^4/\Gamma$。在全纯的背景下,我们考虑了在层次结构的下一个空间上的实例的一个类似的分类,即ALF多taub - nut流形,显示了它们如何通过Nahm对应与Nahm方程的bow解联系在一起。最近Nakajima和Takayama构造了颤振规范理论真空模空间的库仑分支,将它们与弓解的相同空间联系起来。人们可以把我们的构造看作是描述了与Cherkis、O 'Hara和Saemann描述的镜像规范理论的希格斯分支相同的流形。我们的构造也得到了在多taub - nut空间上对于任何经典紧李结构群的全纯瞬子束的单构造。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
36
审稿时长
6-12 weeks
期刊介绍: The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. All major areas of pure mathematics are represented on the editorial board.
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