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Revisiting the Siegel upper half plane II

✍ Scribed by Pedro J. Freitas; Shmuel Friedland

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
307 KB
Volume
376
Category
Article
ISSN
0024-3795

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Revisiting the Siegel upper half plane I
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✍ Shmuel Friedland; Pedro J. Freitas πŸ“‚ Article πŸ“… 2004 πŸ› Elsevier Science 🌐 English βš– 336 KB

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

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Let P s NAM be the minimal parabolic subgroup of SU n q 1, 1 , which can be regarded as the affine automorphism group of the Siegel upper half-plane U nq 1 , P also acts on the Heisenberg group H n , the boundary of U nq 1 . Therefore P has a 2 Ε½ n . 2 Ε½ n . natural representation U on L H . We deco