Journal of Lie Theory, Vol. 9, No. 2, pp. 491-506 (1999)

Spectra of self-gradients on spheres

Thomas Branson

Department of Mathematics, University of Iowa, Iowa City IA 52242, USA

Abstract: We give a general formula for the spectral resolution of a class of first-order differential operators on the sphere $S^n$ which includes, among the most elementary cases, the Dirac and Rarita-Schwinger operators.

Keywords: spectral resolution, first-order differential operators, $n$-sphere, Dirac operator, Rarita-Schwinger operator

Classification (MSC91): 58J50

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