论文标题
通过根系的zeta功能的schur多个反钩类型的zeta功能的表达式
Expressions of Schur multiple zeta-functions of anti-hook type by zeta-functions of root systems
论文作者
论文摘要
我们研究了与半神经代数相关的根系的多个Zeta函数和Zeta功能之间的关系。 Schur多个Zeta函数定义为半标准的年轻Tableaux的总和。然后，假设年轻的tableaux具有反钩状形状，我们表明它们可以用$ a $ a $的根系的修改Zeta命令来编写。我们的证明是相当计算的，但我们也从年轻的Tableaux方面对我们的论点进行了绘画解释。还可以理解，我们的一个定理在Bump等人的意义上通过Weyl ofter多个Dirichlet系列的类似物来表达多个Zeta函数。通过与Nakasuji，Phuksuwan和Yamasaki的结果结合，我们的定理产生了一种新方法，可以在根系的Zeta函数之间找到功能关系。
We investigate relations among Schur multiple zeta functions and zeta-functions of root systems attached to semisimple Lie algebras. Schur multiple zeta functions are defined as sums over semi-standard Young tableaux. Then, assuming the Young tableaux is of anti-hook shape, we show that they can be written in terms of modified zeta-functions of root systems of type $A$. Our proof is quite computational, but we also give a pictorial interpretation of our argument in terms of Young tableaux. It is also possible to understand that one of our theorems gives an expression of Schur multiple zeta functions by an analogue of Weyl group multiple Dirichlet series in the sense of Bump et al. By combining with a result of Nakasuji, Phuksuwan and Yamasaki, our theorems yield a new method of finding functional relations among zeta-functions of root systems.
