PreprintCC BY 4.0arXiv
Quantum Stokes matrices and quantum Riemann-Hilbert-Birkhoff maps
Abstract
In this paper, we define quantum Stokes matrices of meromorphic linear systems of ordinary differential equations with noncommutative coefficients and a pole of order p+1. We prove that these quantum Stokes matrices satisfy natural quantum exchange relations. These relations allow us to interpret the quantum Stokes matrices as an associative algebra homomorphism, which may be viewed as a quantization of the Riemann-Hilbert-Birkhoff map, regarded as a Poisson map, for meromorphic connections.
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BibTeX
@misc{xu2026quantum,
title = {{Quantum Stokes matrices and quantum Riemann-Hilbert-Birkhoff maps}},
author = {Xiaomeng Xu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.31809},
eprint = {2606.31809},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.31809},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Stokes matrices and quantum Riemann-Hilbert-Birkhoff maps
AU - Xiaomeng Xu
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2606.31809
UR - https://arxiv.org/abs/2606.31809
AB - In this paper, we define quantum Stokes matrices of meromorphic linear systems of ordinary differential equations with noncommutative coefficients and a pole of order p+1. We prove that these quantum Stokes matrices satisfy natural quantum exchange relations. These relations allow us to interpret the quantum Stokes matrices as an associative algebra homomorphism, which may be viewed as a quantization of the Riemann-Hilbert-Birkhoff map, regarded as a Poisson map, for meromorphic connections.
ER -