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Lie Groups and Representation Theory
Seminar information archive ～05/01｜Next seminar｜Future seminars 05/02～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2022/01/11
17:00-18:00 Room #on line (Graduate School of Math. Sci. Bldg.)
Joint with Tuesday Seminar on Topology.
Keiichi Maeta (The University of Tokyo)
On the existence problem of Compact Clifford-Klein forms of indecomposable pseudo-Riemannian symmetric spaces with signature (n,2) (Japanese)
Joint with Tuesday Seminar on Topology.
Keiichi Maeta (The University of Tokyo)
On the existence problem of Compact Clifford-Klein forms of indecomposable pseudo-Riemannian symmetric spaces with signature (n,2) (Japanese)
[ Abstract ]
For a homogeneous space $G/H$ and its discontinuous group $\Gamma\subset G$, the double coset space $\Gamma\backslash G/H$ is called a Clifford-Klein form of $G/H$. In the study of Clifford-Klein forms, the classification of homogeneous spaces which admit compact Clifford-Klein forms is one of the important open problems, which was introduced by Toshiyuki Kobayashi in 1980s.
We consider this problem for indecomposable and reducible pseudo-Riemannian symmetric spaces with signature (n,2). We show the non-existence of compact Clifford-Klein forms for some series of symmetric spaces, and construct new compact Clifford-Klein forms of countably infinite five-dimensional pseudo-Riemannian symmetric spaces with signature (3,2).
For a homogeneous space $G/H$ and its discontinuous group $\Gamma\subset G$, the double coset space $\Gamma\backslash G/H$ is called a Clifford-Klein form of $G/H$. In the study of Clifford-Klein forms, the classification of homogeneous spaces which admit compact Clifford-Klein forms is one of the important open problems, which was introduced by Toshiyuki Kobayashi in 1980s.
We consider this problem for indecomposable and reducible pseudo-Riemannian symmetric spaces with signature (n,2). We show the non-existence of compact Clifford-Klein forms for some series of symmetric spaces, and construct new compact Clifford-Klein forms of countably infinite five-dimensional pseudo-Riemannian symmetric spaces with signature (3,2).
