Local Geometric Langlands Correspondence: the Spherical Case
Local Geometric Langlands Correspondence: the Spherical Case
复制标题
局部几何朗兰兹对应：球面情况
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
D. Gaitsgory
中科院分区：
文献类型：
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作者：
E. Frenkel;D. Gaitsgory
一个仿射Kac-Moody代数g^上的模称为球面模，如果李子代数g[[t]]在它上的作用积分为相应群G[[t]]的代数作用。考虑临界水平的球g^-模范畴。本文证明了这一范畴等价于穿孔圆盘上未分歧为局部系统的opers的ind-scheme上的拟凝聚层范畴。这一结果是一个明确的版本，著名的描述球面向量的表示团体在当地的非阿基米德领域。它可以被视为arXiv：math/0508382中提出的局部几何朗兰兹对应的特殊情况。
A module over an affine Kac--Moody algebra g^ is called spherical if the action of the Lie subalgebra g[[t]] on it integrates to an algebraic action of the corresponding group G[[t]]. Consider the category of spherical g^-modules of critical level. In this paper we prove that this category is equivalent to the category of quasi-coherent sheaves on the ind-scheme of opers on the punctured disc which are unramified as local systems. This result is a categorical version of the well-known description of spherical vectors in representations of groups over local non-archimedian fields. It may be viewed as a special case of the local geometric Langlands correspondence proposed in arXiv:math/0508382.