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The concept of Lie algebra and Lie group contractions was introduced into physics by Wigner and Inonu in order to relate the fundamental symmetries of relativistic and non-relativistic physics. This concept has recently been generalised to "graded contractions" of Lie algebras. This contribution is devoted to an application of contractions to relate the separation of variables in spaces of constant nonzero and zero curvature. This leads to asymptotic relations between special functions occurring e.g. in the separation of variables in Laplace-Beltrami equations on spheres and on Euclidean hyperplanes, respectively.
This is based on joint work with J. Patera, G. Pogosyan and
others.
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