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Lattices of minimal covolume in $\operatorname{SL}_2(\mathbb{R}) \times \operatorname{SL}_2(\mathbb{R})$

What are the (uniform/non-uniform) irreducible lattices of minimal (or even small) covolume in $\operatorname{SL}_2(\mathbb{R}) \times \operatorname{SL}_2(\mathbb{R})$? Context: Such a lattice will ...
Stefan Witzel's user avatar
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On the existence of non-arithmetic lattices in algebraic groups over $\mathbb{Q}$

$\newcommand{\Q}{\mathbb{Q}}\newcommand{\R}{\mathbb{R}}\DeclareMathOperator\PU{PU}$Let $G$ be a simple algebraic group over $\Q$ such that $G(\R) \simeq \prod_i G_i$, with each $G_i$ being the Lie ...
naf's user avatar
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Definition of arithmetic subgroups of Lie groups

In Maclachlan-Reid we can read Let $G$ be a connected semisimple Lie group with trivial centre and no compact factor. Let $\Gamma\subset G$ be a discrete subgroup of finite covolume. Then $\Gamma$ is ...
Jacques's user avatar
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Definition of reducible lattice

I am reading Raghunathan's book on discrete subgroups of Lie groups. In particular I am stuck on Corollary 5.19 which gives several equivalent conditions for a lattice in a semisimple Lie group to be ...
user551642's user avatar