On Penney's Cayley transform of a homogeneous Siegel domain

Takaaki Nomura

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13 Citations (Scopus)

Abstract

In this paper we introduce a Cayley transform C of a homogeneous Siegel domain D as a slight modification of Penney's one. We give an explicit formula to the inverse map of C, and thus clarify the biholomorphic nature of C in a direct and visible manner. When D is quasisymmetric, our Cayley transform C is shown to be naturally coincident with Dorfmeister's one. A phenomenon which does not appear in the case of quasisymmetric domains is presented by an example in the last section.

Original languageEnglish
Pages (from-to)185-206
Number of pages22
JournalJournal of Lie Theory
Volume11
Issue number1
Publication statusPublished - 2001
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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