Constructing Buildings and Harmonic Maps
Résumé
In a continuation of our previous work, we outline a theory which should lead to the construction of a universal pre-building and versal building with a $\phi$-harmonic map from a Riemann surface, in the case of two-dimensional buildings for the group $SL(3)$. This will provide a generalization of the space of leaves of the foliation defined by a quadratic differential in the classical theory for $SL(2)$. Our conjectural construction would determine the exponents for $SL(3)$ WKB problems, and it can be put into practice on examples.