Abstract
We showed in [Oh] that for a simple real Lie groupG with real rank at least 2, if a discrete subgroup Γ ofG contains lattices in two opposite horospherical subgroups, then Γ must be a non-uniform arithmetic lattice inG, under some additional assumptions on the horospherical subgroups. Somewhat surprisingly, a similar result is true even if we only assume that Γ contains a lattice in one horospherical subgroup, provided Γ is Zariski dense inG.
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Oh, H. On discrete subgroups containing a lattice in a horospherical subgroup. Isr. J. Math. 110, 333–340 (1999). https://doi.org/10.1007/BF02808188
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DOI: https://doi.org/10.1007/BF02808188