Contractions of Lie algebras and the separation of variables: interbase expansions

Abstract

Lie algebra contractions from o(n + 1) to e(n) are used to obtain asymptotic limits of interbase expansions between bases corresponding to different subgroup chains for the group O(n + 1). The contractions lead to interbase expansions for different subgroup chains of the Euclidean group E(n). They provide asymptotic formulae for quantities such as Wigner rotation matrices, Clebsch-Gordan coefficients and Racah coefficients.