Let $G$ be a real reductive linear Lie group, and $K$ a maximal compact subgroup. Harish-Chandra's renowned admissibility theorem asserts that any irreducible unitary representation of $G$ decomposes into a direct sum of irreducible $K$-modules with each multiplicity finite. In this talk, we discuss to which extent such nice properties hold for a more general setting when we restrict representations to non-compact subgroups $G'$. If time permits, I would like to mention its application to another apparently very different problem, that is, spectral analysis on locally semisimple symmetric spaces.

© Toshiyuki Kobayashi