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On the spectrum of spherical Dirac-type operators. (English) Zbl 1284.53047

Summary: We use polynomial Dirac spinors associated to Euclidean Dirac-type operators and separation of variables to investigate the spectral theory of certain spherical Dirac-type operators. While the spectral theories of our main examples, the spherical Dirac and Laplace-Beltrami operators, are known, this is the first time they are treated together, in a unified manner. In particular, the multiplicities of these spectra, a topic difficult to negotiate in many previous treatments, are presented in simple closed form.

MSC:

53C27 Spin and Spin\({}^c\) geometry
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
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