Action integrals and infinitesimal characters

Details Action integrals and infinitesimal characters Action integrals and infinitesimal characters

2008-08-14

arxiv.org/abs/0808.1955v2

Mathematics

Symplectic Geometry

Completely revised version to appear in Letters in Mathematical Physics

Scientific paper

Let $G$ be a reductive Lie group and ${\mathcal O}$ the coadjoint orbit of a hyperbolic element of ${\frak g}^*$. By $\pi$ 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 $\pi(g)$, for $g\in Z(G)$. We also offer a description of the invariant $\pi(g)$ 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 $\pi$.

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