Hermitian flag manifolds and orbits of the Euclidean group

Arathoon, Philip and Montaldi, James (2015) Hermitian flag manifolds and orbits of the Euclidean group. [MIMS Preprint] (Submitted)

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Abstract

We study the adjoint and coadjoint representations of a class of Lie group including the Euclidean group. Despite the fact that these representations are not in general isomorphic, we show that there is a geometrically defined bijection between the sets of adjoint and coadjoint orbits of such groups. In addition, we show that the corresponding orbits, although different, are homotopy equivalent. We also provide a geometric description of the adjoint and coadjoint orbits of the Euclidean and orthogonal groups as a special class of flag manifold which we call a Hermitian flag manifold. These manifolds consist of flags endowed with complex structures equipped to the quotient spaces that define the flag.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	Adjoint orbits, coadjoint orbits, semi-direct products, Lie groups
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups
Depositing User:	Dr James Montaldi
Date Deposited:	28 Apr 2018 10:26
Last Modified:	28 Apr 2018 10:26
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2635

Available Versions of this Item

• Adjoint and coadjoint orbits of the Euclidean group. (deposited 03 May 2015)
  • Hermitian flag manifolds and orbits of the Euclidean group. (deposited 28 Apr 2018 10:26) [Currently Displayed]

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