
Journal of Lie Theory 16 (2006), No. 1, 047056 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 6068502, Japan kai@math.kyotou.ac.jp 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 [ Fulltextpdf (162 KB)] for subscribers only. 