CONTRACTIONS OF LIE-ALGEBRAS AND SEPARATION OF VARIABLES

The Wigner-Inonu contraction from the rotation group O(3) to the Eucli dean group E(2) is used to relate the separation of variables in the L aplace-Beltrami operators on two corresponding homogeneous spaces. Dif ferent realizations of the contraction take the two separable coordina te systems on the sphere S-2 to the four on the plane E(2).