# A nonhomogeneous orbit closure of a diagonal subgroup | Annals of Mathematics

Abstract Let G=SLl(n,ℝ) with n≥6. We construct examples of lattices Γ⊂G, subgroups A of the diagonal group D and points x∈G/Γ such that the closure of the orbit Ax is not homogeneous and such that the action of A does not factor through the action of a one-parameter nonunipotent group. This contradicts a conjecture of Margulis.

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### 数学年刊（Annals of Mathematics）

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