On the spectrum of spherical Dirac-type operators

Abstract

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.