Expression of the Weyl group multiple Dirichlet series with a solvable lattice models

在这项研究中，我们考虑了杨-巴克斯特方程的应用在很大程度上是在统计力学中可解晶格模型的背景下发展起来的。结果，我们得到了阶乘Schur函数的表达式，它是Schur函数的推广，除了通常的变量外，还有第二组移位参数，作为特定统计力学系统的配分函数，使用Yang-Baxter方程。此外，使用我们的方法，我们给出了阶乘舒尔函数的许多性质的专题证明。另一方面，我们研究了非阿基米德局部域上分裂半单群的球面表示的Iwahori固定向量的某些基，称为Casselman基。我们利用与赫克代数专门化相关的杨-巴克斯特方程得到了它的新表达式。

In this study, we considered the application of the Yang-Baxter equation developed to a large extent in the context of solvable lattice models in statistical mechanics. As a result, we obtain the expression of a factorial Schur function which is generalizations of Schur functions that have, in addition to the usual variables, a second family of shift parameters, as the partition function of a particular statistical mechanical system with using the Yang-Baxter equation. Further, using our methods, we gave thematic proofs of many of the properties of factorial Schur functions.On the other hand, we investigated certain basis of Iwahori fixed vectors of a spherical representation of a split semisimple group over a nonarchimedean local field, called Casselman basis. And we obtained the new expression of that with using Yang-Baxter equation associated to the specializations of the Hecke algebra.