Fenchel-Nielsen twist flows play an important role in Teichmüller theory. They endow Teichmüller space with the structure of a completely integrable system. Twist flows have been generalized to general representation varieties of surface groups by Goldman. However, in the general case, they are not sufficient to provide a completely integrable system, since in this case pairs of pants have additional internal invariants.
In this talk I will introduce new flows on the Hitchin component of SL(n,R). These flows deform the internal invariants of pairs of pants, and together with the twist flows endow the Hitchin component with the structure of a completely integrable system.

This is joint work with Zhe Sun and Tengren Zhang.