Abstract
We construct a new family of flat connections generalising the KZ connection, the Casimir connection and the dynamical connection. These new connections are attached to simply-laced graphs, and are obtained via quantisation of time-dependent Hamiltonian systems controlling the isomonodromic deformations of meromorphic connections on the sphere.
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08 May 2024
A Correction to this paper has been published: https://doi.org/10.1007/s00220-024-04994-9
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Acknowledgements
I express my gratitude to Philip Boalch for suggesting this problem to me. After posting this paper on the arXiv, Daisuke Yamakawa informed me that he has established a result similar to Theorem 7.1, with a different proof [Yam]. This research has been produced while the author was a member of the Laboratoire de Mathématiques d’Orsay, and was funded by a doctoral contract.
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Rembado, G. Simply-Laced Quantum Connections Generalising KZ. Commun. Math. Phys. 368, 1–54 (2019). https://doi.org/10.1007/s00220-019-03420-9
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DOI: https://doi.org/10.1007/s00220-019-03420-9