Real Slices of Parabolic $\mathrm{SL}(r,\mathbb{C})$-Opers

Abstract

Let $X$ be a Riemann surface equipped with an anti-holomorphic involution ${\sigma }_X$. We show that this induces a natural anti-holomorphic involution on the space of parabolic $\mathrm{SL}(r,\mathbb{C})$-opers. The fixed-point locus of this involution is defined as real slice. We further study the induced involutions on different descriptions of parabolic $\mathrm{SL}(r,\mathbb{C})$-opers, in particular differential operators, and prove that these involutions coincide.

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