Timeline for Subgroups of $SL_3(\mathbb{Z})$ that are finitely generated, Zariski-dense, infinite index, and torsion-free
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 19, 2014 at 19:29 | comment | added | Misha | @IgorRivin: I see: Venky handled the case of opposite unipotent lattices in a lattice in the semisimple group (the only case relevant here), while Oh did not make assumptions about the ambient lattice. | |
| Apr 19, 2014 at 18:57 | comment | added | Igor Rivin | Actually, the subject of discrete subgroups with opposite unipotents was started in the (now classical) paper of T.N.Venkataramana in the late '80s. I am not quite certain what the value added in Oh's thesis is, maybe @YvesCornulier knows... | |
| Apr 18, 2014 at 23:58 | vote | accept | Khalid Bou-Rabee | ||
| Apr 18, 2014 at 22:35 | comment | added | Misha | @YvesCornulier: Thanks, I lost track of what Oh knew before her work with Benoist, she covered almost all cases in her PhD thesis, the remaining cases were done with Benoist. | |
| Apr 18, 2014 at 22:33 | comment | added | YCor | @Misha: thanks for the reference to Benoist-Oh (math.u-psud.fr/~benoist/prepubli/09sl3.pdf), t's very interesting. Btw in our case, in their notation, $F_1$ is "reducible", and in this case they give no proof, but refer to an earlier paper of Oh "Discrete subgroups generated by lattices in opposite horospherical subgroups, CRAS 323 (1996)" gauss.math.yale.edu/~ho2/cras.pdf | |
| Apr 18, 2014 at 22:31 | comment | added | Misha | @YvesCornulier: No, even this is unknown. Proving this would be a big step forward (this would answer my question mentioned by OP in the very beginning). | |
| Apr 18, 2014 at 22:20 | comment | added | YCor | @Misha: is it known at least if there's a Zariski-dense representation of $Z^2*Z$ into $SL_3(Z)$ whose restriction to $Z^2$ is faithful, and with image of infinite index? | |
| Apr 18, 2014 at 18:10 | history | edited | Misha | CC BY-SA 3.0 |
added 584 characters in body
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| Apr 18, 2014 at 17:12 | history | answered | Misha | CC BY-SA 3.0 |