Stratified Kaehler structures on adjoint quotients
| dc.creator | Huebschmann, Johannes | |
| dc.date | 2004-04-06 | |
| dc.date | 2006-11-02 | |
| dc.date.accessioned | 2026-07-07T13:08:10Z | |
| dc.date.available | 2026-07-07T13:08:10Z | |
| dc.description | Given a compact Lie group, endowed with a bi-invariant Riemannian metric, its complexification inherits a Kaehler structure having twice the kinetic energy of the metric as its potential, and Kaehler reduction with reference to the adjoint action yields a stratified Kaehler structure on the resulting adjoint quotient. Exploiting classical invariant theory, in particular bisymmetric functions and variants thereof, we explore the singular Poisson-Kaehler geometry of this quotient. Among other things we prove that, for various compact groups, the real coordinate ring of the adjoint quotient is generated, as a Poisson algebra, by the real and imaginary parts of the fundamental characters. We also show that singular Kaehler quantization of the geodesic flow on the reduced level yields the irreducible algebraic characters of the complexified group. | |
| dc.description | AMSTeX2.1, 43 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404141 | |
| dc.identifier | http://arxiv.org/abs/math/0404141 | |
| dc.identifier | Differential Geometry and its Applications 26 (2008) 704-731 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228335 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | 14L24 14L30 17B63 17B65 17B66 17B81 32C20 32Q15 32S05 32S60 53D17 53D20 53D50 81S10 | |
| dc.title | Stratified Kaehler structures on adjoint quotients | |
| dc.type | text |