A loop group method for minimal surfaces in the three-dimensional   Heisenberg group
  We characterize constant mean curvature surfaces in the three-dimensional Heisenberg group by a family of flat connections on the trivial bundle $\D \times \GL$ over a simply connected domain $\mathbb{D}$ in the complex plane. In particular for minimal surfaces, we give an immersion formula, the so-called Sym-formula, and a generalized Weierstrass type representation via the loop group method. 
Josef F. Dorfmeister, Jun-ichi Inoguchi, Shimpei Kobayashi
math.DG