The Cayley transform and uniformly bounded representations |
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Authors: | F Astengo B Di Blasio |
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Institution: | a Dipartimento di Matematica, Università di Genova, 16146 Genova, Italy b School of Mathematics, University of New South Wales, Room 3075, Red Centre, UNSW Sydney 2052, Australia c Dipartimento di Matematica, Università di Roma “Tor Vergata”, 00133 Roma, Italy |
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Abstract: | Let G be a simple Lie group of real rank one, with Iwasawa decomposition and Bruhat big cell . Then the space may be (almost) identified with N and with K/M, and these identifications induce the (generalised) Cayley transform . We show that is a conformal map of Carnot-Caratheodory manifolds, and that composition with the Cayley transform, combined with multiplication by appropriate powers of the Jacobian, induces isomorphisms of Sobolev spaces and . We use this to construct uniformly bounded and slowly growing representations of G. |
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Keywords: | Simple Lie groups of real rank one Cayley transform Uniformly bounded representations |
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