DPW Potentials for Compact Symmetric CMC Surfaces in $\mathbb{S}^3$

Inspired by the work of Heller [12], we show that there exists a DPW potential for the Lawson surface $\xi_{k-1, l-1}$ from which it is possible to reconstruct the minimal immersion $f: \xi_{k-1, l-1} \to \mathbb{S}^3$ via the DPW method. Moreover, we extend the result to surfaces immersed in the 3-sphere with constant mean curvature which satisfy a certain symmetric condition.