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Intertwining operators, the Cayley transform, and the contraction of K to NM

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If you have a question about this talk, please contact Alessio Martini.

The Iwasawa decomposition of a rank one semi-simple Lie group G contains a maximal subgroup K, as well as a semi-direct product NM of a two-step nilpotent group N by a subgroup of K. These two groups are related by the fact that NM is a contraction, a limit of a family of deformations, of K. We use this relationship to compare the two standard pictures of the representations of G: the K picture and the N picture. The representations of MN are in a suitable sense, limits of irreducible representations of K. This observation has consequences for the harmonic analysis of G.

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