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Finite Group Reduction of the DR/DZ Hierarchies
Abstract
We show that the finite group reduction of the Dubrovin-Zhang/Double Ramification hierarchy associated with a semisimple CohFT preserves its bihamiltonian structure and its tau structure. By applying this result to the orbifold Gromov-Witten theory with the target ℙ12,2,2,2, we obtain two non-equivalent integrable hierarchies which can be associated with the Frobenius manifold structure on the Hurwitz space M1;1, and we show that one of them is equivalent to the genus one topological recursion.
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BibTeX
@misc{liu2026finite,
title = {{Finite Group Reduction of the DR/DZ Hierarchies}},
author = {Si-Qi Liu and Youjin Zhang and Tianwen Zhong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.16607},
eprint = {2607.16607},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.16607},
}
RIS
TY - UNPB
TI - Finite Group Reduction of the DR/DZ Hierarchies
AU - Si-Qi Liu
AU - Youjin Zhang
AU - Tianwen Zhong
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2607.16607
UR - https://arxiv.org/abs/2607.16607
AB - We show that the finite group reduction of the Dubrovin-Zhang/Double Ramification hierarchy associated with a semisimple CohFT preserves its bihamiltonian structure and its tau structure. By applying this result to the orbifold Gromov-Witten theory with the target ℙ^1_2,2,2,2, we obtain two non-equivalent integrable hierarchies which can be associated with the Frobenius manifold structure on the Hurwitz space M_1;1, and we show that one of them is equivalent to the genus one topological recursion.
ER -