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摘要翻译：
在这篇注记中，我们讨论了[MTV4]中所得结果的含义。证明了量子gl_N Gaudin模型的Bethe代数的特征向量与多项式核的Fuchsian微分算子是一一对应的。在这里，我们将这一事实解释为gl_N高丁模型中变量的分离。利用多项式核的Fuchsian微分算子，构造了Bethe代数的特征向量。文献[MTV4]表明，如果Gaudin模型的评价参数是泛型的，Bethe代数具有单谱。在这种情况下，我们的Bethe ansatz构造产生了Bethe代数的特征基。
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英文标题：
《On separation of variables and completeness of the Bethe ansatz for
quantum gl_N Gaudin model》
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作者：
E. Mukhin, V. Tarasov, A. Varchenko
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Quantum Algebra 量子代数
分类描述：Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
量子群，skein理论，运算代数和图解代数，量子场论
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
In this note, we discuss implications of the results obtained in [MTV4]. It was shown there that eigenvectors of the Bethe algebra of the quantum gl_N Gaudin model are in a one-to-one correspondence with Fuchsian differential operators with polynomial kernel. Here, we interpret this fact as a separation of variables in the gl_N Gaudin model. Having a Fuchsian differential operator with polynomial kernel, we construct the corresponding eigenvector of the Bethe algebra. It was shown in [MTV4] that the Bethe algebra has simple spectrum if the evaluation parameters of the Gaudin model are generic. In that case, our Bethe ansatz construction produces an eigenbasis of the Bethe algebra.
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PDF链接：
https://arxiv.org/pdf/0712.0981
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