Arathoon, Philip (2015) Coadjoint orbits of the special Euclidean group. Masters thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.
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Abstract
In this report we classify the coadjoint orbits for compact semisimple Lie groups by establishing a correspondence between orbits and subsets of Dynkin diagrams. Particular attention is given to the special unitary and orthogonal groups for which the orbits are complex flags and real Hermitian flags respectively. The orbits for non-compact and nonsemisimple affine groups are discussed and in the example of the special Euclidean group a geometric bijection between adjoint and coadjoint orbits is found.
| Item Type: | Thesis (Masters) |
|---|---|
| Additional Information: | MPhil thesis |
| Uncontrolled Keywords: | flag manifolds, Dynkin diagrams, unitary group, orthogonal group |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry |
| Depositing User: | Dr James Montaldi |
| Date Deposited: | 20 Nov 2015 |
| Last Modified: | 20 Oct 2017 14:13 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2413 |
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