On the Dooley-Rice contraction of the principal series

Abstract

In A. H. Dooley and J. W. Rice: On contractions of semisimple Lie groups}, Trans. Am. Math. Soc., (1985), Dooley and Rice introduced a contraction of the principal series representations of a non-compact semi-simple Lie group to the unitary irreducible representations of its Cartan motion group. We study here this contraction by using non-compact realizations of these representations.