On Penney's Cayley transform of a homogeneous Siegel domain (Q2718666)

The paper deals with Cayley transforms for a homogeneous Siegel domain. Such a ``Cayley transform'' is a biholomorphic map from a given Siegel domain onto a bounded domain, to be chosen as canonical as possible. For symmetric Siegel domains this goes back to the work of Harish-Chandra. Cayley transforms for not necessarily symmetric Siegel domains have been developed by \textit{J. Dorfmeister} [Am. J. Math. 102, 537-563 (1980; Zbl 0441.32013)] and \textit{R. Penney} [Prog. Nonlinear Differ. Equ. Appl. 20, 295-313 (1996; Zbl 0881.32002)].NEWLINENEWLINENEWLINEIn this article a modification of Penney's construction is proposed. This modification has the advantage that the inverse of the ``Cayley transform'' can be described quite explicitly. Furthermore, it is verified that this ``Cayley transform'' coincides with Dorfmeister's construction provided the Siegel domain is quasisymmetric.