Convexity theorems for semisimple symmetric spaces

Abstract

Abstract We prove a convexity theorem for semisimple symmetric spaces G / H ${G/H}$ which generalizes an earlier theorem of the second named author to a setting without restrictions on the minimal parabolic subgroup involved. The new more general result specializes to Kostant’s non-linear convexity theorem for a real semisimple Lie group G in two ways, firstly by taking H maximal compact and secondly by viewing G as a symmetric space for G × G ${G\times G}$ .