Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions
Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions
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DOI：
10.1016/j.geomphys.2019.103571
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发表时间：
2018-09
影响因子：
1.5
通讯作者：
K. Motegi;K. Sakai;Satoshi Watanabe
中科院分区：
文献类型：
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作者：
K. Motegi;K. Sakai;Satoshi Watanabe
本文介绍了Ivanov和Brubaker-Bump-Chinta-Gunnells最近提出的C型和B型冰模型的推广，并用量子逆散射方法详细研究了这两种模型的配分函数.我们使用Izergin-Korepin技术计算波函数的显式形式和它们的导数，该技术可以应用于这两种模型。对于C型冰，我们表明波函数表示使用辛舒尔函数的推广。这给出了一个概括的对应伊万诺夫。对于B型冰，我们证明了波函数的精确表达式是由Bump-Friedberg-Hoffstein引入的Whittaker函数的推广给出的.特殊情况是布鲁贝克-邦普-钦塔-冈内尔斯（Brubaker-Bump-Chinta-Gunnells）记录的通信。我们还显示了这两种模型的畴壁边界配分函数的因式分解形式。作为配分函数研究的结果，我们得到了广义辛Schur函数和广义Whittaker函数的对偶Cauchy公式。
We introduce generalizations of type C and B ice models which were recently introduced by Ivanov and Brubaker–Bump–Chinta–Gunnells, and study in detail the partition functions of the models by using the quantum inverse scattering method. We compute the explicit forms of the wavefunctions and their duals by using the Izergin–Korepin technique, which can be applied to both models. For type C ice, we show the wavefunctions are expressed using generalizations of the symplectic Schur functions. This gives a generalization of the correspondence by Ivanov. For type B ice, we prove that the exact expressions of the wavefunctions are given by generalizations of the Whittaker functions introduced by Bump–Friedberg–Hoffstein. The special case is the correspondence conjectured by Brubaker–Bump–Chinta–Gunnells. We also show the factorized forms for the domain wall boundary partition functions for both models. As a consequence of the studies of the partition functions, we obtain dual Cauchy formulas for the generalized symplectic Schur functions and the generalized Whittaker functions.