Global Plücker formula for W-surfaces associated with simple Lie algebras

Let ${\cal G}$ be an arbitrary simple Lie algebra with Cartan matrix entries $K_{kj}$. Consider a W-surface of genus $g$, with degrees $d_k$ and total ramification numbers $\beta_k$.

Global Plücker formula. For each $k$, one has

$$2g-2-\beta_k+2\sum_{j=1}^n K_{kj}d_j=0.$$

This is proposed as a generalization, to W-surfaces associated with arbitrary simple Lie algebras, of the global Plücker formula. The supplied text does not indicate whether the formula has been proved or remains open.