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

点击翻译按钮获取中文摘要

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.