Abstract: Let be the n-dimensional
Cartan motion group and be the direct limit of the groups endowed with the direct limit
topology. Champetier and Delorme [5] have obtained a characterization of
topologically completely irreducible representation of The aim of this work is to
construct the inductive limit of irreducible representations of and to compute an application to
submodules which generalizes some results showed in [5].
Keywords and phrases: inductive limit of
representations, Cartan motion groups, increasing sequence of groups, G-invariant
spaces.
