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

Dooley, A. H.; Rice, J. W.

Trans. Am. Math. Soc. 289, 185-202 (1985).

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

Keywords:

Riemannian symmetric pair; Cartan motion group; representations; Mehler- Heine formula

References:

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