Timeline for Subgroups of $Sp(2n,\mathbb{R})$ between $Sp(2n,\mathbb{Z})$ and some arithmetic group
Current License: CC BY-SA 3.0
9 events
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| Oct 14, 2016 at 12:49 | history | edited | Venkataramana | CC BY-SA 3.0 |
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| Oct 14, 2016 at 4:55 | history | edited | YCor | CC BY-SA 3.0 |
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| Oct 14, 2016 at 4:36 | history | edited | Venkataramana | CC BY-SA 3.0 |
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| Oct 14, 2016 at 0:15 | comment | added | Venkataramana | @Honing. Thank you ! Yes, in the paper, it was important that it was (usually real) quadratic extension. In general, it seems hard to extend the results of that paper to other extensions. Your question 3 (for real quadratic $K$) is that any intermediate group either has finite index in the larger group or else contains the smaller group as a finite index subgroup (this is weaker than what you have asked for $Sp_{2g}(\mathbb{Z})$). Yes to Question 3, in this weaker sense, implies yes to question 2. | |
| Oct 13, 2016 at 21:06 | vote | accept | Honing | ||
| Oct 13, 2016 at 21:05 | comment | added | Honing | Thank you again! I have three questions if that's ok. 1) Is it important in your paper that $K$ is a real quadratic field? Or could $K$ be any number field? 2) Is it important that $O_K$ is a maximal order in $K$? What if we take any order $O$ and ask a similar question? 3) What if we look at subgroups between $Sp(2g,O_K)$ and some finite index subgroup of $Sp(2g,\mathbb Z)$? Sorry for the many questions; I'm only now discovering these fantastic results. | |
| Oct 13, 2016 at 12:25 | history | edited | Venkataramana | CC BY-SA 3.0 |
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| Oct 13, 2016 at 11:27 | history | edited | Venkataramana | CC BY-SA 3.0 |
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| Oct 13, 2016 at 11:17 | history | answered | Venkataramana | CC BY-SA 3.0 |