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- W2948361505 abstract "We study the monodromy of meromorphic cyclic $mathrm{SL}(n,mathbb{C})$-opers on the Riemann sphere with a single pole. We prove that the monodromy map, sending such an oper to its Stokes data, is an immersion in the case where the order of the pole is a multiple of $n$. To do this, we develop a method based on the work of M. Jimbo, T. Miwa, and K. Ueno from the theory of isomonodromic deformations. Specifically, we introduce a system of equations that is equivalent to the isomonodromy equations of Jimbo-Miwa-Ueno, but which is adapted to the decomposition of the Lie algebra $mathfrak{sl}(n,mathbb{C})$ as a direct sum of irreducible representations of $mathfrak{sl}(2,mathbb{C})$. Using properties of some structure constants for $mathfrak{sl}(n,mathbb{C})$ to analyze this system of equations, we show that deformations of certain families of cyclic $mathrm{SL}(n,mathbb{C})$-opers on the Riemann sphere with a single pole are never infinitesimally isomonodromic." @default.
- W2948361505 created "2019-06-14" @default.
- W2948361505 creator A5004028633 @default.
- W2948361505 date "2019-06-10" @default.
- W2948361505 modified "2023-09-27" @default.
- W2948361505 title "On the Monodromy of Meromorphic Cyclic Opers on the Riemann Sphere" @default.
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