• Corpus ID: 119173130

Frobenius manifolds and quantum groups

  title={Frobenius manifolds and quantum groups},
  author={Xiaomeng Xu},
  journal={arXiv: Mathematical Physics},
  • Xiaomeng Xu
  • Published 30 December 2017
  • Mathematics
  • arXiv: Mathematical Physics
We introduce an isomonodromic Knizhnik-Zamolodchikov connection with respect to the quantum Stokes matrices, and prove that the semiclassical limit of the KZ type connection gives rise to the Dubrovin connections of semisimple Frobenius manifolds. This quantization procedure of Dubrovin connections is parallel to the quantization from Poisson Lie groups to quantum groups, and is conjecturally formulated as a deformation of symplectic transformations on loop spaces in the sense of Givental. 
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