Classification of Toda-type tt*-structures and $\mathbb{Z}_{n+1}$-fixed points

Tadashi Udagawa

Classification of Toda-type tt*-structures and $\mathbb{Z}_{n+1}$-fixed points

Differential Geometry 2025-07-02 v2 High Energy Physics - Theory Mathematical Physics math.MP

Authors: Tadashi Udagawa

Abstract

We classify Toda-type tt*-structures in terms of the anti-symmetry condition. A Toda-type tt*-structure is a flat bundle whose flatness condition is the tt*-Toda equation (Guest-Its-Lin). We show that the Toda-type tt*-structure can be described as a fixed point of $e^{\sqrt{-1}\frac{2\pi}{n+1}}$ -multiplication and this ``intrinsic'' description reduces the possibilities of the anti-symmetry condition to only two cases. We give an application to the relation between tt*-Toda equations and representation theory.

Keywords

fixed point theory vector bundles algebraic topology

Cite

@article{arxiv.2506.23886,
  title  = {Classification of Toda-type tt*-structures and $\mathbb{Z}_{n+1}$-fixed points},
  author = {Tadashi Udagawa},
  journal= {arXiv preprint arXiv:2506.23886},
  year   = {2025}
}

Comments

20 pages. This material has been submitted to Journal of Mathematical Physics. After it is published, it will be found at https://pubs.aip.org/aip/jmp

Classification of Toda-type tt*-structures and $\mathbb{Z}_{n+1}$-fixed points

Abstract

Keywords

Cite

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