Classification of Toda-type tt*-structures and $\mathbb{Z}_{n+1}$-fixed points
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911031552376832 |
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| author | Udagawa, Tadashi |
| author_facet | Udagawa, Tadashi |
| contents | 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 $e^{\sqrt{-1}\frac{2π}{n+1}}$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23886 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of Toda-type tt*-structures and $\mathbb{Z}_{n+1}$-fixed points Udagawa, Tadashi Differential Geometry High Energy Physics - Theory Mathematical Physics 81T40, 53Z05, 17B80 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 $e^{\sqrt{-1}\frac{2π}{n+1}}$-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. |
| title | Classification of Toda-type tt*-structures and $\mathbb{Z}_{n+1}$-fixed points |
| topic | Differential Geometry High Energy Physics - Theory Mathematical Physics 81T40, 53Z05, 17B80 |
| url | https://arxiv.org/abs/2506.23886 |