Abstract
Let G be a Lie group acting on a manifold X and preserving a G-invariant measure. Abstract harmonic analysis seeks to understand the action of G on X by understanding the unitary representation of G on L 2 (X). This may be done by “decomposing” L2 (X) (in an appropriate sense) into irreducible unitary representations. In order to do this, it is useful to have in hand a family of irreducible unitary representations; not necessarily exhaustive, but large enough to solve a range of interesting harmonic analysis problems. The Kirillov-Kostant philosophy of coadjoint orbits seeks to provide such a family. The purpose of these notes is to describe what is known about implementing that philosophy, particularly for reductive groups.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
