Aa. Izmestev et al., CONTRACTIONS OF LIE-ALGEBRAS AND SEPARATION OF VARIABLES, Journal of physics. A, mathematical and general, 29(18), 1996, pp. 5949-5962
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).