Harmonic analysis in vector bundles associated to the rotation and spin groups (Q1188462)

Generalizing some earlier work by \textit{G. Folland} [J. Reine Angew. Math. 398, 130--143 (1989; Zbl 0671.58036)], \textit{S. Gallot} and \textit{D. Meyer} [J. Math. Pur. Appl., IX. Ser. 54, 259--284 (1975; Zbl 0316.53036)], \textit{A. Ikeda} and \textit{Y. Taniguchi} [Osaka J. Math. 15, 515--546 (1978; Zbl 0392.53033)] and \textit{D. B. Ray} [Adv. Math. 4, 109--126 (1970; Zbl 0204.23804)], the author computes the spectrum of the Bochner Laplacian \(\nabla*\nabla\) on any tensor-spinor bundle over \(S^n\), gives the spectrum of the Lichnerowicz Laplacian of any tensor bundle and derives some information about the effect of natural first-order differential operators (generalizing \(d,\delta\) and the Dirac operator) on eigensections of those Laplacians.