In April 2016 Manchester eScholar was replaced by the University of Manchester’s
new Research Information Management System, Pure. In the autumn the University’s research
outputs will be available to search and browse via a new Research Portal. Until then
the University’s full publication record can be accessed via a
temporary portal and the old eScholar content is available to search and browse via this archive.
Related resources
Search for item elsewhere
University researcher(s)
Academic department(s)
Coadjoint Orbits of the Special Euclidean Group
[Thesis]. Manchester, UK: The University of Manchester; 2015.
Access to files
-
FULL-TEXT.PDF (pdf)
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 non-semisimple affine groups are discussed and in the example of the special Euclidean group a geometric bijection between adjoint and coadjoint orbits is found.
Keyword(s)
Bibliographic metadata
Type of resource:
Content type:
Form of thesis:
Type of submission:
Thesis title:
Degree type:
Master of Philosophy
Degree programme:
MPhil Mathematical Sciences
Publication date:
Institution:
Location:
Manchester, UK
Total pages:
55
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 non-semisimple affine groups are discussed and in the example of the special Euclidean
group a geometric bijection between adjoint and coadjoint orbits is found.
Keyword(s):
Thesis main supervisor(s):
Thesis co-supervisor(s):
Degree grantor:
Language:
en
Institutional metadata
University researcher(s):
Academic department(s):
Record metadata
Manchester eScholar ID:
uk-ac-man-scw:277589
Created by:
Arathoon, Philip
Created:
10th November, 2015, 11:55:43
Last modified by:
Arathoon, Philip
Last modified:
1st December, 2017, 09:08:07