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On contractions of semisimple Lie groups. (English) Zbl 0546.22017

Let (G,K) be a Riemannian symmetric pair of the compact or noncompact type and let \(V\rtimes K\) be the associated Cartan motion group. This article shows how to obtain the representations of \(V\rtimes K\) from the representations of G, using the fact that \(V\rtimes K\) is a contraction of G. The results obtained generalize to an arbitrary matrix coefficient the classical Mehler-Heine formula.

MSC:

22E46 Semisimple Lie groups and their representations
57S99 Topological transformation groups
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