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The general theory of coset manifolds (coset formalism) is defined. The notion of parallel transport and general relativity on the coset manifold are explained. In particular, one has a notion of H-covariant Lie derivatives. Finally, rigid superspace is obtained as a particular type of coset manifold, using this formalism.
We define the notion of spherical harmonics, as a generalization from the two-sphere case. We use coset theory to define them, and then we describe examples of spherical harmonics. The KK decomposition is defined, and then the particular cases of groups spaces and spheres are considered for the spherical harmonics.
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