Appears in collection : 2025 - T1 - WS3 - Analysis on homogeneous spaces and operator algebras

When a Lie group $G$ acts transitively on a manifold $X$, an irreducible subrepresentation of the unitary representation $L^2(X)$ is called a discrete series representation of $X$. The discrete series plays an important role in the study of harmonic analysis for symmetric spaces. In this talk, we would like to give sufficient conditions for the existence of discrete series for general homogeneous spaces of real reductive groups and also for the case of equivariant line bundles in terms of coadjoint orbits.