Three sides of the geometric Langlands correspondence for gl_N Gaudin model and Bethe vector averaging maps
Three sides of the geometric Langlands correspondence for gl_N Gaudin model and Bethe vector averaging maps
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gl_N Gaudin 模型和 Bethe 向量平均图的几何 Langlands 对应关系的三边
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
A. Varchenko
中科院分区：
文献类型：
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作者：
E. Mukhin;V. Tarasov;A. Varchenko
我们考虑标准向量表示的张量幂的gl_N Gaudin模型. Gaudin模型中的几何朗兰兹对应关系将交换Gaudin Hamilton算子的Bethe代数与适当的N阶微分算子空间上的函数代数联系起来。在本文中，我们介绍了第三方面的对应关系：代数的职能的关键集的一个主功能。我们构造了第三代数和前两个代数的同构。
一个新的对象是贝特矢量平均图。
We consider the gl_N Gaudin model of a tensor power of the standard vector representation. The geometric Langlands correspondence in the Gaudin model relates the Bethe algebra of the commuting Gaudin Hamiltonians and the algebra of functions on a suitable space of N-th order differential operators. In this paper we introduce a third side of the correspondence: the algebra of functions on the critical set of a master function. We construct isomorphisms of the third algebra and the first two.
A new object is the Bethe vector averaging maps.