Analytic vector harmonic expansions on S U (2) and S2

Abstract

Irreducible vector fields (vector harmonics) are introduced on SU (2). It is shown that an arbitrary vector field can be expanded in terms of these vector harmonics, and tight convergence conditions are derived for analytic vector fields. These expansions are related to well−known vector harmonic expansions on the two−sphere. The generalization to arbitrary tensor fields is discussed. A connection between the Lie algebra of vector fields on SU (2) and the Virasoro algebra is noted.