2008/08/14 by Andrés Viña, Viña, Andrés
Mathematics · #22E45 #53D50 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.0808.1955
openalex publication_date 2008/08/14 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/31
Let G be a reductive Lie group and \mathcal O the coadjoint orbit of a hyperbolic element of \frak g^*. By π is denoted the unitary irreducible representation of G associated with \mathcal O by the orbit method. We give geometric interpretations in terms of concepts related to \mathcal O of the constant π(g), for g∈ Z(G). We also offer a description of the invariant π(g) in terms of action integrals and Berry phases. In the spirit of the orbit method we interpret geometrically the infinitesimal character of the differential representation of π.