Revisiting the Siegel upper half plane I

✍ Scribed by Shmuel Friedland; Pedro J. Freitas

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 336 KB
• Volume: 376
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(03)00662-1

✦ Synopsis

In the first part of the paper we show that the Busemann 1-compactification of the Siegel upper half plane of rank n : SH n = Sp(n, R)/K n is the compactification as a bounded domain. In the second part of the paper we study certain properties of discrete groups of biholomorphisms of SH n . We show that the the set of accumulation points of the orbit (Z) on the Shilov boundary of SH n is independent of Z, and denote this set by ( ). We associate with the standard class of Patterson-Sullivan (PS) p-measures. For p-regular these measures are supported on ( ). For 1-regular PS 1-measures are conformal densities. For , with ( ) / = ∅, we give a modified version of the class of PS measures, which are always supported on ( ).