Convexity theorems for symmetric spaces and representations of n-Lie algebras. Two studies in Lie theory

Abstract

This thesis is a thesis in Lie theory. The thesis is split into two parts. The first part classifies the irreducible highest-weight representations of the simple n-Lie algebra. The theorem proven in this part contains precisly the before-mentioned classification. The main theorem of the thesis is contained in the second part and represents a generalisation of the non-linear convexity result of Kostant to semisimple symmetric spaces.