Constructing Buildings and Harmonic Maps

Ludmil Katzarkov (1) , Alexander Noll (1) , Pranav Pandit , Carlos Simpson (2)

1 Universität Wien = University of Vienna
2 LJAD - Laboratoire Jean Alexandre Dieudonné

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.

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Ludmil Katzarkov, Alexander Noll, Pranav Pandit, Carlos Simpson. Constructing Buildings and Harmonic Maps. Algèbre, Géométrie et Physique : une conférence en l'honneur de Maxim Kontsevitch , Jun 2014, Paris, France. ⟨hal-01331629⟩