The classical and quantum particle on a flag manifold

Abstract

In the present paper we consider two related problems, i.e. the description of geodesics and the calculation of the spectrum of the Laplace-Beltrami operator on a flag manifold. We show that there exists a family of invariant metrics such that both problems can be solved simply and explicitly. In order to determine the spectrum of the Laplace-Beltrami operator, we construct natural, finite-dimensional approximations (of spin chain type) to the Hilbert space of functions on a flag manifold.

40 pages, 11 figures

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Cited by in corpus (1)

• Oscillator Calculus on Coadjoint Orbits and Index Theorems