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Journal of Lie Theory 11 (2001), No. 1, 185--206
Copyright Heldermann Verlag 2001

On Penney's Cayley Transform of a Homogeneous Siegel Domain

Takaaki Nomura
Dept. of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan

We introduce a Cayley transform C of a homogeneous Siegel domain D as a slight modification of Penney's one. We give an explicit formula to the inverse map of C, and thus clarify the biholomorphic nature of C in a direct and visible manner. When D is quasisymmetric, our Cayley transform C is shown to be naturally coincident with Dorfmeister's one. A phenomenon which does not appear in the case of quasisymmetric domains is presented by an example in the last section.

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