Tohoku Mathematical Journal
2007

March
SECOND SERIES VOL. 59, NO. 1

Tohoku Math. J.
59 (2007), 101-118

Title A CHARACTERIZATION OF SYMMETRIC SIEGEL DOMAINS BY CONVEXITY OF CAYLEY TRANSFORM IMAGES

Author Chifune Kai

(Received February 2, 2006, revised May 17, 2006)
Abstract. We show that a homogeneous Siegel domain is symmetric if and only if its Cayley transform image is convex. Moreover, this convexity forces the parameter of the Cayley transform to be specific, so that the Cayley transform coincides with the inverse of the Cayley transform introduced by Korányi and Wolf.

2000 Mathematics Subject Classification. Primary 32M15; Secondary 43A85, 32H02.

Key words and phrases. Homogeneous Siegel domain, symmetric Siegel domain, Cayley transform, normal $j$-algebra.

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