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John Pardon
John Pardon
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Lattices in $SL(n,\mathbb{R} R)$

Does there existIf $\Gamma\subseteq SL(n,\mathbb{R})$ is a lattice in $SL(n,\mathbb{R})$ which(i.e. discrete and finite covolume), does not$\Gamma$ necessarily contain anysome $\mathbb{R}$-diagonalizable copy of $\mathbb{Z}^{n-1}$  ? I

I know that the answer is noyes if the lattice is supposed to be uniformcocompact, and that $SL(n,\mathbb{Z})$ also satisfies this property, that the answer is whyalso yes in the case $\Gamma=SL(n,\mathbb Z)$. So I wonder if every lattice satisfies this property.

Lattices in $SL(n,\mathbb{R})

Does there exist a lattice in $SL(n,\mathbb{R})$ which does not contain any $\mathbb{R}$-diagonalizable copy of $\mathbb{Z}^{n-1}$  ? I know that the answer is no if the lattice is supposed to be uniform, and that $SL(n,\mathbb{Z})$ also satisfies this property, that is why I wonder if every lattice satisfies this property.

Lattices in $SL(n,\mathbb R)$

If $\Gamma\subseteq SL(n,\mathbb{R})$ is a lattice (i.e. discrete and finite covolume), does $\Gamma$ necessarily contain some $\mathbb{R}$-diagonalizable copy of $\mathbb{Z}^{n-1}$?

I know that the answer is yes if the lattice is cocompact, and that the answer is also yes in the case $\Gamma=SL(n,\mathbb Z)$. So I wonder if every lattice satisfies this property.

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ALB
ALB
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Lattices in $SL(n,\mathbb{R})

Does there exist a lattice in $SL(n,\mathbb{R})$ which does not contain any $\mathbb{R}$-diagonalizable copy of $\mathbb{Z}^{n-1}$ ? I know that the answer is no if the lattice is supposed to be uniform, and that $SL(n,\mathbb{Z})$ also satisfies this property, that is why I wonder if every lattice satisfies this property.