Growth of homogeneous spaces, density of discrete subgroups and Kazhdan's property \((T)\) (Q1803379)
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scientific article; zbMATH DE number 220746
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Growth of homogeneous spaces, density of discrete subgroups and Kazhdan's property \((T)\) |
scientific article; zbMATH DE number 220746 |
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Growth of homogeneous spaces, density of discrete subgroups and Kazhdan's property \((T)\) (English)
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29 June 1993
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It is shown that if \(G\) is a semisimple Lie group with finite center and no compact factors and if \(H\) is a closed unimodular subgroup of \(G\) such that \(G/H\) has subexponential volume growth, then \(H\) is Zariski dense in \(G\). Moreover, if \(G\) has Kazhdan's property \((T)\) then \(G/H\) must have finite volume. The results are extended to semisimple groups over a local field.
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growth the homogeneous spaces
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density of discrete subgroups
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semisimple Lie group
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Kazhdan's property (T)
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local field
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0.8837743
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0.87047863
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0.8686714
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0.8654988
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0.86536574
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0.8653238
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