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SEPARATION OF VARIABLES AND LIE-ALGEBRA CONTRACTIONS. APPLICATIONS TO SPECIAL FUNCTIONS

G. Pogosyan
Centro de Ciencias Fisicas Universidad Nacional Autonoma de Mexico, Morelos, Mexico
Joint Institute for Nuclear Research, Dubna
International Center for Advanced Studies, Yerevan State University, Yerevan, Armenia


A. Sissakian
Joint Institute for Nuclear Research, Dubna

P. Winternitz
Centre de recherches mathematiques, Universite de Montreal, Montreal, Quebec, Canada

A review is given of some recently obtained results on analytic contractions of Lie algebras and Lie groups and their application to special function theory. The contractions considered are from O(3) to E(2) and from O(2,1) to E(2), or E(1,1). The analytic contractions provide relations between separable coordinate systems on various homogeneous manifolds. They lead to asymptotic relations between basis functions and overlap functions for the representations of different groups.


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