Simple root flows for Hitchin representations

Martin Bridgeman (1) , Richard Canary (2) , François Labourie (3, 4) , Andres Sambarino (5)

1 BC - Boston College
2 Department of Mathematics - University of Michigan
3 LJAD - Laboratoire Jean Alexandre Dieudonné
4 LM-Orsay - Laboratoire de Mathématiques d'Orsay
5 UP11 - Université Paris-Sud - Paris 11

We study simple root flows and Liouville currents for Hitchin representations. We show that the Liouville current is associated to the measure of maximal entropy for a simple root flow, derive a Liouville volume rigidity result, and construct a Liouville pressure metric on the Hitchin component.

Domaines: Géométrie différentielle [math.DG]; Topologie géométrique [math.GT]

Martin Bridgeman, Richard Canary, François Labourie, Andres Sambarino. Simple root flows for Hitchin representations. Geometriae Dedicata, 2018, ⟨10.1007/s10711-017-0305-2⟩. ⟨hal-01654560⟩