Contraction of an adapted functional calculus. (English) Zbl 0882.22015

Cotton, P.; Dooley, A. H.

J. Lie Theory 7, No. 2, 147-164 (1997).

Authors’ summary: “We aim to show, using the example of a Riemannian symmetric pair \((G,K)=(SL_2(\mathbb{R}),SO(2))\), 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 \(V\ltimes K\), 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 A. H. Dooley and J. W. Rice [Trans. Am. Math. Soc. 289, 185-202 (1985; Zbl 0566.22015)]”.

Reviewer: W.M.McGovern (Seattle)

MSC:

22E46	Semisimple Lie groups and their representations
22E43	Structure and representation of the Lorentz group

Keywords:

functional calculus; contraction; principal series; generic orbits; coadjoint orbits; Lie groups; representations

Citations:

Zbl 0566.22015