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.
Publié le : 2007-05-14
Classification:
Homogeneous Siegel domain,
symmetric Siegel domain,
Cayley transform,
normal $j$-algebra,
32M15,
43A85,
32H02
@article{1176734750,
author = {Kai, Chifune},
title = {A characterization of symmetric Siegel domains by convexity of Cayley transform images},
journal = {Tohoku Math. J. (2)},
volume = {59},
number = {1},
year = {2007},
pages = { 101-118},
language = {en},
url = {http://dml.mathdoc.fr/item/1176734750}
}
Kai, Chifune. A characterization of symmetric Siegel domains by convexity of Cayley transform images. Tohoku Math. J. (2), Tome 59 (2007) no. 1, pp. 101-118. http://gdmltest.u-ga.fr/item/1176734750/