Discrete Miura Opers and Solutions of the Bethe Ansatz Equations
Discrete Miura Opers and Solutions of the Bethe Ansatz Equations
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Bethe Ansatz 方程的离散 Miura 算子和解
DOI：
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发表时间：
2004
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;A. Varchenko
与单李代数的XXX模型相关的贝特假设方程的解以被称为“族”的形式出现。我们证明一个族同构于朗兰兹对偶李代数的旗簇。证明基于贝特假设方程的解与我们称为离散三浦算子的特殊差分算子之间的对应关系。离散三浦算子的概念是本文的主要结果之一。对于与一个族中的一个点相关联的离散三浦算子D，我们表明差分方程DY = 0的所有解都是有理函数，并且这些解可以根据构成该族的点明确地写出。
Solutions of the Bethe ansatz equations associated to the XXX model of a simple Lie algebra come in families called the populations. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra The proof is based on the correspondence between the solutions of the Bethe ansatz equations and special difference operators which we call the discrete Miura opers. The notion of a discrete Miura oper is one of the main results of the paper.For a discrete Miura oper D, associated to a point of a population, we show that all solutions of the difference equation DY=0 are rational functions, and the solutions can be written explicitly in terms of points composing the population.