Redding, Nigel2017-08-012017-08-012017http://hdl.handle.net/10393/36467http://dx.doi.org/10.20381/ruor-20747In this thesis, we study the polynomial equations that describe the highest weight orbit of an irreducible finite dimensional highest weight module under a semisimple Lie group. We also study the connection of the convex hull of this orbit and the Carathéodory orbitope.enOrbitopesRepresentation TheoryThesis