Results 1 
3 of
3
Tessellations of homogeneous spaces of classical groups of real rank two
, 2008
"... Let H be a closed, connected subgroup of a connected, simple Lie group G with finite center. The homogeneous space G/H has a tessellation if there is a discrete subgroup Γ of G, such that Γ acts properly discontinuously on G/H, and the doublecoset space Γ\G/H is compact. Note that if either H or ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
Let H be a closed, connected subgroup of a connected, simple Lie group G with finite center. The homogeneous space G/H has a tessellation if there is a discrete subgroup Γ of G, such that Γ acts properly discontinuously on G/H, and the doublecoset space Γ\G/H is compact. Note that if either H or G/H is compact, then G/H has a tessellation; these are the obvious examples. It is not difficult to see that if G has real rank one, then only the obvious homogeneous spaces have tessellations. Thus, the first interesting case is when G has real rank two. In particular, R. Kulkarni and T. Kobayashi constructed examples that are not obvious when G = SO(2, 2n) ◦ or SU(2, 2n). H. Oh and D. Witte constructed additional examples in both of these cases, and obtained a complete classification when G = SO(2, 2n) ◦. We simplify the work of OhWitte, and extend it to obtain a complete classification when G = SU(2, 2n). This includes the construction of another family of examples. The main results are obtained from methods of Y. Benoist and T. Kobayashi: we fix a Cartan decomposition G = KA + K, and study the intersection (KHK) ∩ A +. Our exposition generally assumes only the standard theory of connected Lie groups, although basic