Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation and Bethe vectors
Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation and Bethe vectors
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量化 Knizhnik-Zamolodchikov 方程和 Bethe 向量的渐近解
DOI：
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发表时间：
1994
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：
V. Tarasov;A. Varchenko
构造了与$\mathfrak{gl}_{N + 1}$相关的量子化克尼兹尼克 - 扎莫罗德奇科夫方程的渐近解。渐近解的首项是贝塞向量——量子自旋链模型转移矩阵的一个本征向量。我们表明贝塞向量的范数等于一个适当函数的黑塞矩阵与一个明确写出的有理函数的乘积。这个公式是贝塞向量范数的高汀 - 科列平公式的类似物。表明在一般情况下，对于$\mathfrak{gl}_2$情形，贝塞向量构成一个基。
Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation associated with $frak{gl}_{N+1}$ are constructed. The leading term of an asymptotic solution is the Bethe vector -- an eigenvector of the transfer-matrix of a quantum spin chain model. We show that the norm of the Bethe vector is equal to the product of the Hessian of a suitable function and an explicitly written rational function. This formula is an analogue of the Gaudin-Korepin formula for the norm of the Bethe vector. It is shown that, generically, the Bethe vectors form a base for the $frak{gl}_2$ case.