SLOW ENTROPY OF HIGHER RANK ABELIAN UNIPOTENT ACTIONS

. We study slow entropy invariants for abelian unipotent actions U on any finite volume homogeneous space G/Gamma. For every such action we show that the topological slow entropy can be computed directly from the dimension of a special decomposition of Lie(G) induced by Lie(U). Moreover, we are able to show that the metric slow entropy of the action coincides with its topological slow entropy. As a corollary, we obtain that the complexity of any abelian horocyclic action is only related to the dimension of G. This generalizes the rank one results from [14] to higher rank abelian actions.