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arXiv · 2607.16607

Finite Group Reduction of the DR/DZ Hierarchies

Si-Qi Liu·Youjin Zhang·Tianwen Zhong
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Abstract

We show that the finite group reduction of the Dubrovin-Zhang/Double Ramification hierarchy associated to a semisimple CohFT preserves its bihamiltonian structure and its tau structure. By applying this result to the orbifold Gromov-Witten theory with the target $\mathbb{P}^1_{2,2,2,2}$, we see that there are two different and interesting integrable hierarchies that can be associated to the Frobenius manifold structure on the Hurwitz space $M_{1;1}$. One of them is equivalent to the genus $1$ topological recursion.

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Si-Qi Liu, Youjin Zhang, Tianwen Zhong. 2026-07-18. Finite Group Reduction of the DR/DZ Hierarchies. https://arxiv.org/abs/2607.16607

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