Local geometric Langlands correspondence and affine Kac-Moody algebras
Local geometric Langlands correspondence and affine Kac-Moody algebras
复制标题
局部几何 Langlands 对应和仿射 Kac-Moody 代数
DOI：
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发表时间：
2005
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
设（mathfrak{g}）是环G上的单李代数，G是具有李代数（mathfrak{g}）的连通代数群.仿射Kac-Moody代数（hat {mathfrak{g}}）是形式循环代数（mathfrak{g}）（（t））的泛中心扩张.（hat {mathfrak{g}}）的表示有一个参数，一个关于（mathfrak{g}）的不变双线性形式，它被称为水平。对应于等于Killing型的负一半的双线性型的表示称为临界水平表示。这样的表示可以在环群G（（t））与其“开紧”子群K的商上的扭D-模的整体截面空间中实现，例如G[[t]]或Iwahori子群I。
Let ( mathfrak{g} ) be a simple Lie algebra over ℂ and G a connected algebraic group with Lie algebra ( mathfrak{g} ). The affine Kac-Moody algebra ( hat {mathfrak{g}} ) is the universal central extension of the formal loop agebra ( mathfrak{g} )((t)). Representations of ( hat {mathfrak{g}} ) have a parameter, an invariant bilinear form on ( mathfrak{g} ), which is called the level. Representations corresponding to the bilinear form which is equal to minus one half of the Killing form are called representations of critical level. Such representations can be realized in spaces of global sections of twisted D-modules on the quotient of the loop group G((t)) by its “open compact” subgroup K, such as G[[t]] or the Iwahori subgroup I.