2018/04/25 by Philip Arathoon, Arathoon, Philip, James Montaldi +1
Mathematics · #22E15 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1804.09463
openalex publication_date 2018/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.