Positive Energy Representations, Holomorphic Discrete Series and Finite-Dimensional Irreps

Understand

Let G be a semi-simple non-compact Lie group with unitary lowest/highest weight representations.

• We consider explicitly the relation between three types of representations of G: positive energy (unitary lowest weight)representations, (holomorphic) discrete series representations and non-unitary finite-dimensional irreps.
• We consider mainly the conformal groups SO(n,2) treating in full detail the cases n=1,3,4.