Extended Schur's Q-functions and the full Kostant-Toda hierarchy on the Lie algebra of type D

被引：1

作者：

Kodama, Yuji ^{[1
,2
]}

Okada, Soichi ^{[3
]}

机构：

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

[2] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

[3] Nagoya Univ, Grad Sch Math, Nagoya 4648602, Japan

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2023年 / 443卷

基金：

日本学术振兴会;

关键词：

The full Kostant-Toda hierarchy; Schur's Q-functions; Polynomial tau-functions; Pfaffian invariants; LATTICE; SYSTEMS;

D O I：

10.1016/j.physd.2022.133589

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 all the polynomial Tau-functions of the hierarchy.(c) 2022 Elsevier B.V. All rights reserved.

引用

页数：13