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Journal of Lie Theory 16 (2006), No. 1, 047--056
Copyright Heldermann Verlag 2006

Symmetry Characterization of Quasisymmetric Siegel Domains by Convexity of Cayley Transform Images

Chifune Kai
Dept. of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan

We characterize symmetric Siegel domains among quasisymmetric Siegel domains by means of the Cayley transform introduced by Dorfmeister. We show that a quasisymmetric Siegel domain is symmetric if and only if its Cayley transform image is convex.

Keywords: Quasisymmetric Siegel domain, symmetric Siegel domain, Cayley transform, Jordan algebra.

MSC: 32M15; 32H02, 43A85

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