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Journal of Lie Theory, 7(2), 147-164 (1997)
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Contraction of an adapted functional calculus

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P. Cotton and A. H. Dooley

Department of Mathematics

Stanford University

Stanford CA 94305

U.S.A.

cotton@gauss.Stanford.edu School of Mathematics

University of New South Wales

NSW 2052

Australia

A.Dooley@unsw.edu.au

**Abstract:** We aim to show, using the example Riemannian symmetric pair $(G,K) = (\SLTWOR,\SOTWO)$, how contraction ideas may be applied to functional calculi constructed on coadjoint orbits of Lie groups. We construct such calculi on principal series orbits and generic orbits of the Cartan motion group $V\rtimes K$, and show how the two are related. Since the calculi are adapted to the representations traditionally attached to the orbits, we recover at the Lie algebra level the contraction results of Dooley and Rice.
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