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We study the monodromy of meromorphic cyclic   $\textrm{SL}(n,{\mathbb{C}})$  -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 Jimbo, Miwa, and 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   $\textrm{SL}(n,\mathbb{C})$  -opers on the Riemann sphere with a single pole are never infinitesimally isomonodromic.

On the Monodromy of Meromorphic Cyclic Opers on the Riemann Sphere