Spin structures on compact simply connected Riemannian symmetric spaces. (English) Zbl 0677.53057

The authors study the existence of spin structures on compact simply connected symmetric spaces G/K of compact type. At first they list these spaces for the case of the classical simple groups. Then they describe the connection between the spectral decomposition of the Dirac operator and representation theory of G, given by Frobenius reciprocity. The rest of the paper is devoted to a complete list of the compact symmetric spaces corresponding to the exceptional simple groups which admit a spin structure.
Reviewer: J.Eichhorn


53C35 Differential geometry of symmetric spaces
58J50 Spectral problems; spectral geometry; scattering theory on manifolds