Title: Fock-Goncharov coordinates for rank 2 Lie groups
2016.06.21 |
| Date | Tue 28 Jun |
| Time | 13:00 — 14:00 |
| Location | 1532-122 (Aud. G2) |
Abstract
We discuss the higher Teichmuller space A_{G,S} defined by Fock and Goncharov. This space is defined for a punctured surface S with negative Euler characteristic, and a semisimple, simply connected Lie group G. There is a birational atlas on A_{G,S} with a chart for each ideal triangulation of S. Fock and Goncharov showed that the transition functions are positive, i.e. subtraction-free rational functions. We will show that when G has rank 2, the transition functions are given by explicit quiver mutations.
We discuss the higher Teichmuller space A_{G,S} defined by Fock and Goncharov. This space is defined for a punctured surface S with negative Euler characteristic, and a semisimple, simply connected Lie group G. There is a birational atlas on A_{G,S} with a chart for each ideal triangulation of S. Fock and Goncharov showed that the transition functions are positive, i.e. subtraction-free rational functions. We will show that when G has rank 2, the transition functions are given by explicit quiver mutations.
