Discrete series representation

Summary

A discrete series representation of a locally compact group $G$ is an irreducible unitary representation. It occurs as a direct summand of the regular representation on $L^2(G)$. These are the representations that contribute point masses to the Plancherel measure. Let $G$ be a connected semisimple Lie group with finite center. Harish-Chandra showed that $G$ has discrete series exactly when it has a compact Cartan subgroup, and he classified them. They are the building blocks from which the Langlands classification constructs all irreducible admissible representations.