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Talk Abstract

Contractions of Lie Algebras and the Separation of Variables

Contractions of Lie Algebras and the Separation of Variables

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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