Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve
Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve
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非阿贝尔霍奇曲线理论中的镜像对称性和朗兰兹对偶性
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发表时间：
2004
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通讯作者：
Tamás Hausel
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文献类型：
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作者：
Tamás Hausel
本文分别考察了Hausel-Thaddeus和Hausel-Rodriguez-Villegas关于SL（n，n）与PGL（n，n）平坦联络和曲线的特征标簇的某些Hodge数相等的镜像对称性.解释了几个新的结果和结构以及它们与希钦、戈滕、加西亚-海曼和厄尔-基尔万的工作的关系。这些使用表示理论的有限群的李型通过算术的字符品种，并导致一个意想不到的猜想硬莱夫谢茨定理的上同调。
The paper surveys the mirror symmetry conjectures of Hausel-Thaddeus and Hausel-Rodriguez-Villegas concerning the equality of certain Hodge numbers of SL(n, ℂ) vs. PGL(n, ℂ) flat connections and character varieties for curves, respectively. Several new results and conjectures and their relations to works of Hitchin, Gothen, Garsia-Haiman and Earl-Kirwan are explained. These use the representation theory of finite groups of Lie-type via the arithmetic of character varieties and lead to an unexpected conjecture for a Hard Lefschetz theorem for their cohomology.