Tessellations of homogeneous spaces of classical groups of real rank two

Details Tessellations of homogeneous spaces of classical groups of real rank two Tessellations of homogeneous spaces of classical groups of real rank two

2001-02-25

arxiv.org/abs/math/0102191v1

Mathematics

Representation Theory

74 pages, 7 figures

Scientific paper

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 D of G, such that D acts properly discontinuously on G/H, and the double-coset space D\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 Oh-Witte, 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 = KAK, and study the intersection of KHK with A. Our exposition generally assumes only the standard theory of connected Lie groups, although basic properties of real algebraic groups are sometimes also employed; the specialized techniques that we use are developed from a fairly elementary level.

Affiliated with

Also associated with

No associations

Rating

Tessellations of homogeneous spaces of classical groups of real rank two does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Tessellations of homogeneous spaces of classical groups of real rank two, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tessellations of homogeneous spaces of classical groups of real rank two will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-383372