Constructing Buildings and Harmonic Maps

Abstract

In a continuation of our previous work [21], we outline a theory which should lead to the construction of a universal pre-building and versal building with a φ-harmonic map from a Riemann surface, in the case of twodimensional buildings for the group SL₃. This will provide a generalization of the space of leaves of the foliation defined by a quadratic differential in the classical theory for SL₂. Our conjectural construction would determine the exponents for SL₃ WKB problems, and it can be put into practice on examples.

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