Contractions of Lie algebras and separation of variables

Abstract

The Wigner - Inonu contraction from the rotation group O(3) to the Euclidean group E(2) is used to relate the separation of variables in the Laplace - Beltrami operators on two corresponding homogeneous spaces. Different realizations of the contraction take the two separable coordinate systems on the sphere 0305-4470/29/18/024/img7 to the four on the plane 0305-4470/29/18/024/img8.