Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590253 | Journal of Functional Analysis | 2014 | 25 Pages |
Abstract
Let G be a real reductive Lie group, let H=TAH=TA be the identity component of a Cartan subgroup, and let hh be the corresponding Cartan subalgebra. This leads to a parabolic subgroup of G whose identity component is MAN. The unitary G-representations induced by MAN are known as the H -series. We study symplectic geometry of G×hG×h and apply geometric quantization to construct unitary G-representations by partially harmonic forms. They are direct integrals of the H-series, indexed by the image of the moment map. We also perform symplectic reduction and symplectic induction, and consider their analogues in representation theory via geometric quantization.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Meng-Kiat Chuah,