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 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.
Mathematics Subject Classification (2010).
- Primary: 14H30; Secondary: 34E20
- Grothendieck topology
- polyhedral complex
- spectral curve
- spectral network
- BPS state
- WKB exponent