Exact WKB and abelianization for the $T_3$ equation

@article{Hollands2019ExactWA,
  title={Exact WKB and abelianization for the \$T_3\$ equation},
  author={Lotte Hollands and A. Neitzke},
  journal={arXiv: High Energy Physics - Theory},
  year={2019}
}
We describe the exact WKB method from the point of view of abelianization, both for Schrodinger operators and for their higher-order analogues (opers). The main new example which we consider is the "$T_3$ equation," an order $3$ equation on the thrice-punctured sphere, with regular singularities at the punctures. In this case the exact WKB analysis leads to consideration of a new sort of Darboux coordinate system on a moduli space of flat $\mathrm{SL}(3)$-connections. We give the simplest… Expand
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