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首页> 外文期刊>Journal of geometry and physics >Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions
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Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions

机译：互相频散散射法和互相梭函数的概念和惠特克函数

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We introduce generalizations of type C and B ice models which were recently introduced by lvanov 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 wave-functions 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 lvanov. 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. (C) 2019 Elsevier B.V. All rights reserved.
机译：我们介绍了最近由Lvanov和Brubaker-Bump-Chinta-Gunnells引入的C型和B ICE模型的概括，并通过使用量子逆散射方法详细研究模型的分区功能。我们使用Izergin-Korepin技术计算波浪函数的显式形式和它们的双重型，这可以应用于两种型号。对于C型冰，我们显示了使用辛舒尔函数的概括来表达的波力事件。这给出了Lvanov的通信概括。对于B型冰，我们证明了波力事件的确切表达是通过撞击器函数的概括来给出的，通过撞击器的函数的概括来给出。特别案件是Brubaker-Bump-Chinta-Gunnells召集的通信。我们还显示两个模型的域墙边界分区功能的分解形式。由于分区函数的研究，我们获得了用于广义辛SCHUR功能的双Cauchy公式和广义惠特克函数。 （c）2019年Elsevier B.V.保留所有权利。

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