Real Slices of Parabolic SL(r,C)-Opers

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.