论文标题
扩展Schur的$ Q $ functions和全部Kostant- type $ d $的Lie代数的高潮层次结构
Extended Schur's $Q$-functions and the full Kostant--Toda hierarchy on the Lie algebra of type $D$
论文作者
论文摘要
半神经元素上的全部Kostant-Toda层次结构是一个宽松方程的系统，其中流量由Chevalley不变性的梯度确定。本文涉及完整的Kostant-Tabo-Toda-toda-toda-toda-toda-toda-toda-toda-toda-toda-toda层。通过将Lax矩阵的PFAFFIAN作为Chevalley不变式之一，我们构建了与此不变性相关的流动的明确形式。作为主要结果，我们在时间变量中介绍了Schur的$ Q $函数的扩展，并使用它们为层次结构的多项式$τ$ functions提供明确的公式。
The full Kostant--Toda hierarchy on a semisimple Lie algebra is a system of Lax equations, in which the flows are determined by the gradients of the Chevalley invariants.This paper is concerned with the full Kostant--Toda hierarchy on the even orthogonal Lie algebra. By using a Pfaffian of the Lax matrix as one of the Chevalley invariants, we construct an explicit form of the flow associated to this invariant. As a main result, we introduce an extension of the Schur's $Q$-functions in the time variables, and use them to give explicit formulas for the polynomial $τ$-functions of the hierarchy.
