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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.

DOI Code: 10.1285/i15900932v33n2p83

Keywords: Contraction of Lie groups; contraction of representations; semi-simple Lie group; semi-direct product; Cartan motion group; unitary representation; principal series; coadjoint orbit.

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