Kostant, Steinberg, and the Stokes matrices of the tt*-Toda equations

Martin A. Guest, Nan Kuo Ho*

*この研究の対応する著者

研究成果査読

2 被引用数 (Scopus)

抄録

We propose a Lie-theoretic definition of the tt*-Toda equations for any complex simple Lie algebra g, based on the concept of topological–antitopological fusion which was introduced by Cecotti and Vafa. Our main results concern the Stokes data of a certain meromorphic connection, whose isomonodromic deformations are controlled by these equations. First, by exploiting a framework introduced by Boalch, we show that this data has a remarkable structure. It can be described using Kostant’s theory of Cartan subalgebras in apposition and Steinberg’s theory of conjugacy classes of regular elements, and it can be visualized on the Coxeter Plane. Second, we compute canonical Stokes data for a certain family of solutions of the tt*-Toda equations in terms of their asymptotics. To do this, we compute the Stokes data of an auxiliary meromorphic connection, related to the original meromorphic connection by a loop group Iwasawa factorization.

本文言語English
論文番号50
ジャーナルSelecta Mathematica, New Series
25
3
DOI
出版ステータスPublished - 2019 8 1

ASJC Scopus subject areas

  • 数学 (全般)
  • 物理学および天文学(全般)

フィンガープリント

「Kostant, Steinberg, and the Stokes matrices of the tt*-Toda equations」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル