Global Weyl groups and a new theory of multiplicative quiver varieties
Global Weyl groups and a new theory of multiplicative quiver varieties
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全局Weyl群和乘法箭簇新理论
DOI：
10.2140/gt.2015.19.3467
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发表时间：
2013
影响因子：
2
通讯作者：
P. Boalch
中科院分区：
文献类型：
--
作者：
P. Boalch
在以前的工作中，建立了一大类Kac-Moody代数与全局曲线上的亚纯连接之间的关系——值得注意的是Weyl群给出了连接的不同模空间之间的同构，并且根系统也被认为发挥了作用。这涉及到许多中岛颤振变体的模解释，作为连接的模空间，只要底层图是完全k部图（或更一般的超新星图）。然而，在同构故事或野生非abel Hodge理论中，考虑了稍大的连接模空间。这就提出了一个问题，即满模空间是否承认Weyl群同构，而不仅仅是开放部分与颤振变体同构。通过开发前面方法的“乘法版本”，这个问题将在这里得到解决。这相当于在野生性状品种之间构造许多代数辛同构。这种方法也使我们能够对某些不规则的Deligne—Simpson问题提出一个猜想，并引入一些非交换代数，推广了“广义双仿射Hecke代数”。
In previous work a relation between a large class of Kac-Moody algebras and meromorphic connections on global curves was established---notably the Weyl group gives isomorphisms between different moduli spaces of connections, and the root system is also seen to play a role. This involved a modular interpretation of many Nakajima quiver varieties, as moduli spaces of connections, whenever the underlying graph was a complete k-partite graph (or more generally a supernova graph). However in the isomonodromy story, or wild nonabelian Hodge theory, slightly larger moduli spaces of connections are considered. This raises the question of whether the full moduli spaces admit Weyl group isomorphisms, rather than just the open parts isomorphic to quiver varieties. This question will be solved here, by developing a "multiplicative version" of the previous approach. This amounts to constructing many algebraic symplectic isomorphisms between wild character varieties. This approach also enables us to state a conjecture for certain irregular Deligne--Simpson problems and introduce some noncommutative algebras, generalising the "generalised double affine Hecke algebras".
作为希格斯丛和局部系统模的希尔伯特方案
影响因子：
1
作者：
Groechenig M
通讯作者：
Groechenig M