Coadjoint Orbits of the Special Euclidean Group

  • Philip Arathoon

Student thesis: Master of Philosophy


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.
Date of Award3 Jan 2016
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorJames Montaldi (Supervisor) & Yuri Bazlov (Supervisor)


  • Lie groups
  • adjoint orbits
  • coadjoint orbits

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