Abstract
Let G be a reductive Lie group and \({{\mathcal O}}\) the coadjoint orbit of a hyperbolic element of \({{\frak g}^*}\) . The unitary irreducible representation of G associated with \({{\mathcal O}}\) by the orbit method is denoted by π. We give geometric interpretations in terms of concepts related to \({{\mathcal O}}\) of the constant π(g), for \({g \in Z(G)}\) . 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 geometrically interpret the infinitesimal character of the differential representation of π.
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This work was partially supported by Ministerio de Educación y Ciencia, grant MAT2007-65097-C02-02.
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Viña, A. Action Integrals and Infinitesimal Characters. Lett Math Phys 91, 241–264 (2010). https://doi.org/10.1007/s11005-010-0372-x
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DOI: https://doi.org/10.1007/s11005-010-0372-x