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Using an integrable discrete Dirac operator, we construct a discrete versionof the Weierstrass representation of time-like surfaces parametrized alongisotropic directions in $R^{2,1}$, $R^{3,1}$ and $R^{2,2}$. The correspondingdiscrete surfaces have isotropic edges. We show that any discrete surfacesatisfying a general monotonicity condition and having isotropic edges admitssuch a representation.

The Weierstrass representation of discrete isotropic surfaces in $R^{2,1}$, $R^{3,1}$ and $R^{2,2}$