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

Tadashi Udagawa

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arXiv · 2506.23886

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

Tadashi Udagawa

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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.

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Tadashi Udagawa. 2025-06-30. Classification of Toda-type tt*-structures and $\mathbb{Z}_{n+1}$-fixed points. https://arxiv.org/abs/2506.23886

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