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Convergence and semisimplicity of big quantum cohomology of flag varieties

  • Changzheng Li
  • Zhaoyang Liu
  • Tony Yue Yu
  • Chi Zhang
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Abstract

We prove the folklore conjecture that the big quantum cohomology of a flag variety G/P of general Lie type is convergent near the large-radius limit and is generically semisimple. The convergence relies on a slightly modified version of Iritani's reconstruction theorem, together with Cauchy's formula that avoids directly taking the non-equivariant limit at the origin. Generic semisimplicity follows from a surprising application of the big quantum D-module mirror symmetry for G/P established by the first, third and fourth authors jointly with Hinault and Zhang. Moreover, we prove the regularity conjecture on the big quantum cohomology of G/P formulated by Perrin and Smirnov, which implies generic semisimplicity.

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Cite

BibTeXRIS
BibTeX
@misc{li2026convergence,
  title = {{Convergence and semisimplicity of big quantum cohomology of flag varieties}},
  author = {Changzheng Li and Zhaoyang Liu and Tony Yue Yu and Chi Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28418},
  eprint = {2610.28418},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28418},
}
RIS
TY  - UNPB
TI  - Convergence and semisimplicity of big quantum cohomology of flag varieties
AU  - Changzheng Li
AU  - Zhaoyang Liu
AU  - Tony Yue Yu
AU  - Chi Zhang
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28418
UR  - https://arxiv.org/abs/2610.28418
AB  - We prove the folklore conjecture that the big quantum cohomology of a flag variety G/P of general Lie type is convergent near the large-radius limit and is generically semisimple. The convergence relies on a slightly modified version of Iritani's reconstruction theorem, together with Cauchy's formula that avoids directly taking the non-equivariant limit at the origin. Generic semisimplicity follows from a surprising application of the big quantum D-module mirror symmetry for G/P established by the first, third and fourth authors jointly with Hinault and Zhang. Moreover, we prove the regularity conjecture on the big quantum cohomology of G/P formulated by Perrin and Smirnov, which implies generic semisimplicity.
ER  -